BANA 2372 - Chapter 5
A weighted average of the value of a random variable, where the probability function provides weights is known as
the expected value
A weighted average of the value of a random variable, where the probability function provides weights, is known as _____.
the expected value
X is a random variable with the probability function: f(X) = X/6 for X = 1, 2 or 3 The expected value of X is
2.333
The _______ of the discrete random variable X is a measure of the dispersion or variability of a probability distribution V(X) = E(X - E(X))^2 = sum [(x - E(X))^2f(x) = sum[x^2f(x) - E(X)^2
variance
The standard deviation of a binomial distribution is a. (x) = P(1 - P) b. (x) = nP c. (x) = nP(1 - P) d. None of these alternatives is correct.
None of these alternatives is correct.
The expected value for a binomial distribution is
Np
As the number of trials (n) in a binomial experiment increases to infinity while the binomial mean (np) remains constant, the binomial distribution becomes the __________ distribution. note: require consistent units
Poisson
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The random variable x satisfies which of the following probability distributions?
Poisson
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-8. The random variable x satisfies which of the following Discrete Probability Distributions?
Poisson
When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a
Poisson distribution
If the mean and variance of a data set are not about the same, then the ________ ____ ____ _______ model would not be a good representation of that set E(X) = λ σ^2 = V(X) = λ
Poisson mean and variance
The weight of an object is an example of
a continuous random variable
The weight of an object measured in grams is an example of
a continuous random variable
The weight of an object, measured in grams, is an example of _____.
a continuous random variable
The Poisson probability distribution is used with
a discrete random variable
The binomial probability distribution is used with
a discrete random variable
The number of customers that enter a store during one day is an example of
a discrete random variable
The number of customers who enter a store during one day is an example of _____.
a discrete random variable
The weight of an object, measured to the nearest gram, is an example of _____.
a discrete random variable
binomial probability distribution is used with _____.
a discrete random variable
variance is
a measure of the dispersion of a a random variable
Variance is
a measure of the dispersion of a random variable
An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a
continuous random variable
An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. this is a
continuous random variable
The average annual incomes of high school and college graduates in a Midwestern town are $21,000 and $35,000, respectively. If a company hires only personnel with at least a high school diploma and 20% of its employees have been through college, what is the mean income of the company employees?
$23,800
An experiment consists of making 80 telephone calls in order to sell a particular insurance policy.
discrete random variable
An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a
discrete random variable
A random variable X has a ________ ________ _________ if each of the n values in its range, say, x1, x2, .... , xn, has equal probability. Then, f(xi) = 1/n
discrete uniform distribution
The expected value of a discrete random variable
is the average value for the random variable over many repeats of the experiment
The expected value of a discrete random variable _____.
is the average value for the random variable over many repeats of the experiment.
Bivariate probabilities are often called _____.
joint probabilities
The implication of using a geometric model is that the system presumably will not wear out. The probability of an error remains constant for all transmissions. This is called the ________ _____ ________ property.
lack of memory
4% of the customers of a mortgage company default on their payments. a sample of 5 is selected, what is the prob. of 2 defaulting
.0142
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?
.0413
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 6 are male?
.0499
The following represents the probability distribution for the daily demand of computers at a local store. Demand Probability 0 0.1 1 0.2 2 0.3 3 0.2 4 0.2 Refer to Exhibit 5-1. The probability of having a demand for at least two computers is
0.7
The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. Number of Fatal Accidents Number of Days 0 45 1 75 2 120 3 45 4 15 Refer to Exhibit 5-12. What is the probability that in a given day there will be at least 1 accident?
0.85
The variance Var(x) for the binomial distribution is
np(1 − p)
The probability distribution for the daily sales at Michael's Co. is given below. Daily Sales ($1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 Refer to Exhibit 5-2. The probability of having sales of at least $50,000 is
0.90
A description of how the probabilities are distributed over the values the random variable can assume is called a(n) _____.
probability distribution
A description of the distribution of the values of a random variable and their associated probabilities is called a
probability distribution
The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number Of Goals Probability 0 0.05 1 0.15 2 0.35 3 0.30 4 0.15 Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score at least 1 goal?
0.95
The key difference between binomial and hypergeometric distributions is that with the hypergeometric distribution the _____.
probability of success changes from trial to trial
In a binomial experiment, the _____.
probability of success does not change from trial to trial
A main goal in statistics is to interpret and understand the meaning of statistical values. The _______ can be very helpful in understanding the meaning of the mean and standard deviation.
range rule of thumb
Which of the following are true statements? I. By the law of large numbers, the mean of a random variable will get closer and closer to a specific value. II. The standard deviation of a random variable is never negative. III. The standard deviation of a random variable is zero only if the random variable takes a single value.
I, II, and III
The standard deviation of a binomial distribution is _____.
None of the answers are correct (below) -E(x) = pn(1 − n) -E(x) = np(1 − p) -E(x) = np
In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the
Poisson distribution
In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that models this situation is the
Poisson distribution
Which of the following statements about a discrete random variable and its probability distribution are true?
Values of f(x) must be greater than or equal to zero.
Which of the following statements about a discrete random variable and its probability distribution is true?
Values of f(x) must be greater than or equal to zero.
In a binomial experiment, the probability of success is .06. What is the probability of two successes in seven trials?
.0554
In a binomial experiment the prob. of success is .06. What is the prob. of two successes in seven trials.
.0555
The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. Refer to Exhibit 5-11. The probability there are 8 occurrences in 10 minutes is _____.
.0771
The probability Pete will catch fish when he goes fishing is .8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly 1 day is _____.
.096
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. Refer to Exhibit 5-7. The probability that Pete will catch fish on exactly one day is
.096
A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
0.0038
Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?
0.0142
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-2. What is the probability that among the students in the sample exactly two are female?
0.0413
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 6 are male?
0.0499
The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number Of Goals Probability 0 0.05 1 0.15 2 0.35 3 0.30 4 0.15 Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score no goals?
0.05
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
0.0778
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-2. What is the probability that among the students in the sample at least
0.1064
A binomial probability distribution with p = 0.3 is _____.
negatively skewed
The standard deviation is the _____.
positive square root of the variance
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Refer to Exhibit 5-9. What is the random variable in this experiment?
the number of female voters out of 5
In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?
0.0554
Find the probability that a family of five children will have exactly three boys.
.3125
A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a
binomial probability distribution
A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a _____.
binomial probability distribution
Identify the expression for calculating the mean of a binomial distribution.
np
The binomial probability distribution is most symmetric when _____.
p equals 0.5
A numerical description of the outcome of an experiment is called a _____.
random variable
An example of a bivariate experiment is _____.
rolling a pair of dice
Which of the following is not a property of a binomial experiment?
the probabilities of the two outcomes can change from one trial to the next
Which of the following is NOT one of the three methods for finding binomial probabilities that is found in the chapter on discrete probability distributions?
using a simulation
Which of the following is NOT a required condition for a discrete probability function?
∑f(x) = 0
Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X is normally distributed with a mean of $360 and standard deviation of $50. What is the z- score that corresponds to the likelihood of the profit of $400?
.80
If the probability of a basketball player scoring on any shot is .75, what is the probability that she will score on at most 5 of her next 6 shots?
.8220
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below: Number of Breakdowns Probability 0 0.12 1 0.38 2 0.25 3 0.18 4 0.07 Refer to Exhibit 5-11. The probability of no breakdowns in a month is
0.12
The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. Number of Fatal Accidents Number of Days 0 45 1 75 2 120 3 45 4 15 Refer to Exhibit 5-12. What is the probability that in a given day there will be no accidents?
0.15
The probability Pete will catch fish when he goes fishing is .8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The expected number of days Pete will catch fish is _____.
2.4
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. Refer to Exhibit 5-7. The expected number of days Pete will catch fish is
2.4
A department store has determined in connection with its inventory control that the demand for a certain CD player averages 4 per day. If the store stocks 5 of these items on a particular day, what is the probability that demand will exceed supply?
2150
Probability Distribution x f(x) 10 .2 20 .3 30 .4 40 .1 Refer to Exhibit 5-5. The expected value of x equals
24
The United States Senate has 100 members. Suppose there are 54 Republicans and 46 Democrats. A committee of 15 Senators is selected at random. What is the expected number of Republicans on this committee?
8.1
Probability Distribution x f(x) 10 .2 20 .3 30 .4 40 .1 Refer to Exhibit 5-5. The variance of x equals
84
The prob. of sales at least of 50000
90%
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee Frequency 0 700 1 900 2 600 3 300 2,500 Refer to Exhibit 5-6. The variance of the number of cups of coffee is
96
Which of the following would be information in a question asking you to find the area of a region under the standard normal curve as a solution?
A distance on the horizontal axis is given
A trial with only two possible outcomes. Usually assumed that the trials that constitute the random experiment are independent. Often reasonable to assume that the probability of a success in each trial is constant.
Bernoulli trial
Indicate a similarity between a Poisson distribution and a binomial distribution.
Both distributions have an independence requirement.
An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is the number of sales made. This random variable is a
Discrete random variable
Geometric mean and variance
E(X) = 1/p σ^2 = V(X) = (1-p)/p^2
binomial mean and variance
E(X) = n*p V(X) = np(1-p)
The expected value for a binomial probability distribution is
E(x) = nP
The expected value for a binomial probability distribution is _____.
E(x) = np
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. Refer to Exhibit 5-7. The variance of the number of days Pete will catch fish is
.48
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee Frequency 0 700 1 900 2 600 3 300 Total 2,500 Refer to Exhibit 5-7. The variance of the number of cups of coffee is
.96
Finding probabilities associated with distributions that are standard normal distributions is equivalent to _______.
finding the area of the shaded region representing that probability
The ________ of the discrete random variable X is a measure of the center of a probability distribution E(X) = sum x*f(x)
mean
Which of the following is NOT a requirement for a density curve?
the graph is centered around 0
Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
the trials are dependent
Which of the following is a characteristic of a binomial experiment?
the trials are independent
A continuous random variable has a _______ distribution if its values are spread evenly over the range of possibilities.
uniform
The variance for the binomial probability distribution is
var(x) = nP(1 - P)
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The probability that there are 8 occurrences in ten minutes is
.0771
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-8. The probability that there are 8 occurrences in ten minutes is
.0771
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Refer to Exhibit 5-9. The probability that there are no females in the sample is _____.
.0778
The primary air exchange system on a proposed spacecraft has four separate components (call them A, B, C, and D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = 0.95, P(B) = 0.90, P(C) = 0.99, and P(D) = 0.90. Find the probability that the entire system works properly
.7618
If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of 4 successes in 15 trials, the correct probability function to use is the
binomial probability function
If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of two successes in 15 trials, the correct probability function to use is the _____.
binomial probability function
Excel's BINOM.DIST function can be used to compute _____.
both binomial probabilities and cumulative binomial probabilities
An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a
continuous random variable
Highway patrol officers measure the speed of automobiles on a highway using radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a _____.
continuous random variable
The _______ _______ ______ of a discrete random variable X, denoted F(x), is F(x) = P(X <= x) = sum (xi <= x) f(xi) F(x) satisfies the following properties 1) F(x) = P(X <= x) = sum (xi <= x) f(xi) 2) 0 <= F(x) <= 1 3) if x< = y, then F(x) <= F(y)
cumulative distribution function
Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?
exactly two outcomes are possible on each trial
A measure of the average value of a random variable is called
expected value
A measure of the average value of a random variable is called a(n)
expected value
A measure of the average value of a random variable is called a(n) _____.
expected value
A weighted average of the value of a random variable where the prob. function provides weights is known as
expected value
Which of the following is not a required condition for a discrete probability function?
f(x) = 0 for all values of x
Which of the following is a required condition for a discrete probability function?
f(x) = 1 for all values of x
Poisson probability mass function
f(x) = e^-(λ)*λ^x/x! for x = 1, 2,...
To compute a binomial probability. we must know all of the following except the _____.
number of elements in the population
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. What is the random variable in this experiment?
the number of days out of 3 that Pete catches fish
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the random variable in this experiment?
the number of female students out of 8
In a binomial experiment
the probability does not change from trial to trial
The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution
the probability of success changes from trial to trial
The key difference between the binomial and hypergeometric distribution is that, with the hypergeometric distribution
the probability of success changes from trial to trial.
The notation P(z<a) denotes _______.
the probability that Z score is less than A
A continuous random variable may assume
any value in an interval or collection of intervals
A continuous random variable may assume _____.
any value in an interval or collection of intervals
A continuous random variable may assume:
any value in an interval or collection of intervals
A random experiment consisting of n Bernoulli trials such that: 1) the trials are independent 2) each trial only results in two possibilities, labelled as "success" or "failure" 3) the probability of a success in each trial, denoted as p, remains constant probability mass function: f(x) = Cp(1-p)^n-x for x=0,1,2,...,n binomial expansion: (a+b)^n = sum Ca^kb^n-k
binomial distribution definition
An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a
continuous random variable.
_______ _________ such as P(X <= x) can be useful in finding the probability mass function of a random variable an alternative method of describing the probability distribution of a random variable
cumulative probabilities
The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. Refer to Exhibit 5-11. The appropriate probability distribution for the random variable is _____.
discrete
Which of the following groups of terms can be used interchangeably when working with normal distributions?
areas, probability, and relative frequencies
Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.
continuous
A random variable that may take on any value in an interval or collection of intervals is known as a
continuous random variable
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-8. The appropriate probability distribution for the random variable is
discrete
The Poisson probability distribution is a
discrete probability distribution
An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is 0.2 and having a major accident is 0.05, how much can the insurance company expect to make on the policy? (Expected profit)
$350
The probability distribution for the daily sales at Michael's Co. is given below. Daily Sales (In $1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 Refer to Exhibit 5-9. The expected daily sales are
$56,000
Excel's BINOM.DIST function has how many inputs?
4
Different distributions could have the same mean & variance.
True
A random variable that can assume only a finite # of values is
discrete random variable
The standard deviation is the
positive square root of the variance
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below. Number of Probability Breakdowns 0 0.12 1 0.38 2 0.25 3 0.18 4 0.07 Refer to Exhibit 5-4. The probability of no breakdowns in a month is
*None of the alternative answers is correct
The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. Refer to Exhibit 5-11. The probability there are less than 3 occurrences is _____.
.1016
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The probability that there are less than 3 occurrences is
.1016
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-8. The probability that there are less than 3 occurrences is
.1016
The probability Pete will catch fish when he goes fishing is .8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The probability that Pete will catch fish on 1 or fewer days is _____.
.104
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. Refer to Exhibit 5-7. The probability that Pete will catch fish on one day or less is
.104
The accident rate in a factory is 4 per month. What is the probability that there will be 6 accidents in a particular month?
.1042
There are 13 Democrats, 12 Republicans, and 8 Independents sitting in a room. Eight of these people will be selected to serve on a special committee. What is the probability that exactly five of the committee members will be Democrats?
.10567
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 7 are female?
.1064
The telephone sales department of a certain store receives an average of 24 calls per hour. What is the probability that between 10:00 a.m. and 10:05 a.m. there will be 3 calls?
.1804
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Refer to Exhibit 5-9. The probability that the sample contains 2 female voters is _____.
.3456
If three people, Joe, Betsy, and Sue, play a game in which Joe has a 25% chance of winning and Betsy has a 40% chance of winning, what is the probability that Sue will win? (There is only one winner and no ties.)
.35
A medicine is known to produce side effects for 1 in 5 patients taking it. Suppose a doctor prescribes the medicine to 4 unrelated patients. What is the probability that none of the patients will develop side effects?
.4096
The probability Pete will catch fish when he goes fishing is .8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is _____.
.48
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below: Number of Breakdowns Probability 0 0.12 1 0.38 2 0.25 3 0.18 4 0.07 Refer to Exhibit 5-11. The probability of at least 3 breakdowns in a month is
0.25
The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution. x f(x) 0 0.80 1 0.15 2 0.04 3 0.01 The mean and the standard deviation for the number of electrical outages (respectively) are
0.26 and 0.577
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Refer to Exhibit 5-4. The probability that the sample contains 2 female voters is
0.3456
The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number Of Goals Probability 0 0.05 1 0.15 2 0.35 3 0.30 4 0.15 Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score less than 3 goals?
0.55
Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below. Production Per Month Probability x f(x) 1 0.01 2 0.04 3 0.10 4 0.80 5 0.05 Refer to Exhibit 5-13. The standard deviation for the production is
0.612
The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. Number of Fatal Accidents Number of Days 0 45 1 75 2 120 3 45 4 15 Refer to Exhibit 5-12. What is the probability that in a given day there will be less than 3 accidents?
0.8
The probability distribution for the daily sales at Michael's Co. is given below. Daily Sales (In $1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 Refer to Exhibit 5-9. The probability of having sales of at least $50,000 is
0.90
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee Frequency 0 700 1 900 2 600 3 300 2,500 Refer to Exhibit 5-6. The expected number of cups of coffee is
1.2
Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee Frequency 0 700 1 900 2 600 3 300 Total 2,500 Refer to Exhibit 5-7. The expected number of cups of coffee is
1.2
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-3. The standard deviation is
1.431
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below: Number of Breakdowns Probability 0 0.12 1 0.38 2 0.25 3 0.18 4 0.07 Refer to Exhibit 5-11. The expected number of machine breakdowns per month is
1.70
Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is
12
Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is _____.
12
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-3. The variance is
2.047
The following represents the probability distribution for the daily demand of computers at a local store. Demand Probability 0 0.1 1 0.2 2 0.3 3 0.2 4 0.2 Refer to Exhibit 5-1. The expected daily demand is
2.2
x is a random variable with the prob. function f(x) = x/6 for x = 1,2 or 3. the expected value of x is
2.333
x is a random variable with the probability function: f(x) = x/6 for x = 1, 2, or 3. The expected value of x is _____.
2.333
The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number Of Goals Probability 0 0.05 1 0.15 2 0.35 3 0.30 4 0.15 Refer to Exhibit 5-10. The expected number of goals per game is
2.35
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-3. The expected number of new clients per month is
3.05
Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below. Production Per Month Probability x f(x) 1 0.01 2 0.04 3 0.10 4 0.80 5 0.05 Refer to Exhibit 5-13. the expected monthly production level is
3.84
Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is
4
Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is _____.
4
Excel's HYPGEOM.DIST function has how many inputs?
5
If calculations are time-consuming and if a sample size is no more than 5% of the size of the population, the _______ states to treat the selections as being independent (even if the selections are technically dependent).
5% Guideline for Cumbersome Calculations
The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. Refer to Exhibit 5-11. The expected value of the random variable x is _____.
5.3
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-8. The expected value of the random variable x is
5.3
Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value of this distribution is
50
Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value of this distribution is _____.
50
The prob. distribution for the daily sales are given, what are the expected daily sales
56,000
In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is _____.
6
In the binomial probability formula, the variable x represents the
In the binomial probability formula, the variable x represents the number of successes.
Which of the following is a discrete random variable?
The number of times a student guesses the answers to questions on a certain test
The expected value of a random variable is the _____.
None of the answers are correct (below) -value of the random variable that should be observed on the next repeat of the experiment -value of the random variable that occurs most frequently -square root of the variance
Which of the following is(are) required condition(s) for a discrete probability function?
None of the answers are correct (below)∑f(x) = 0f(x) ≥ 1 for all values of xf(x) < 0
The expected value of a random variable is A)the value of the random variable that occurs most frequently B)the square root of the variance C)the value of the random variable that should be observed on the next repeat of the experiment D)None of these alternatives is correct.
None of these alternatives is correct.
The expected value of a random variable is a. the value of the random variable that should be observed on the next repeat of the experiment b. the value of the random variable that occurs most frequently c. the square root of the variance d. None of these alternatives is correct.
None of these alternatives is correct.
The hypergeometric probability distribution is identical to a. the Poisson probability distribution b. the binomial probability distribution c. the normal distribution d. None of these alternatives is correct.
None of these alternatives is correct.
Which of the following statements about discrete distributions is not true?
When calculating probabilities for discrete distributions, p(x < 1) and the P(x ≤ 1) will result in the same value.
If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the
Poisson probability distribution
The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. The random variable x satisfies the
Poisson probability distribution.
The _______ _______ of the random variable X is a description of the probabilities with the possible numerical values of X
Probability distributions
Excel's _____ function can be used to compute the expected value of a discrete random variable.
SUMPRODUCT
Excel's _____ function can be used to compute the variance of a discrete random variable.
SUMPRODUCT
For the binomial distribution, which formula finds the standard deviation?
Square root of npq
The standard deviation of the Poisson distribution is calculated using _______.
Square root of u
Which of the following is NOT a descriptor of a normal distribution of a random variable?
The graph is centered around 0.
Which of the following does NOT describe the standard normal distribution?
The graph is uniform.
Which of the following is not true of discrete probability distributions?
The graph of the distribution always exhibits symmetry.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The mean and standard deviation have the values of 0 and 1
Which one of these variables is a discrete random variable?
The number of unbroken eggs in a carton
Which of the following is NOT a requirement of the Poisson Distribution?
The occurrences must be dependent.
Which of the following is NOT a property of a binomial experiment?
The probabilities of the two outcomes can change from one trial to the next.
Which of the following properties of a binomial experiment is called the stationarity?
The probability of success is the same for each trial.
Which one of these variables is a continuous random variable?
The time it takes a randomly selected student to complete an exam
Which of the following is NOT a characteristic of an experiment where the binomial probability distribution is applicable?
The trials are dependent.
Which of the following is not a requirement of the binomial probability distribution?
The trials must be dependent.
The variance for the binomial probability distribution is _____.
Var(x) = np(1 − p)
When using Excel's BINOM.DIST function, one should choose TRUE for the fourth input if _____.
a cumulative probability is desired
When using Excel's HYPGEOM.DIST function, one should choose TRUE for the fifth input if _____.
a cumulative probability is desired
Variance is _____.
a measure of the dispersion of a random variable
A marketing manager instructs his team to make 80 telephone calls to attempt to sell an insurance policy. The random variable in this experiment is the number of sales made. This random variable is a _____.
discrete random variable
A random variable that can assume only a finite number of values is referred to as a(n)
discrete random variable
A random variable that can assume only a finite number of values is referred to as a(n) _____.
discrete random variable
An experiment consists of making 80 calls in order to sell a particular insurance policy. The random variable in this experiment is the # of sales made. This random variable is a
discrete random variable
The # of customers that enter a store during one day is an example of
discrete random variable
The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. The appropriate probability distribution for the random variable is
discrete.
_________ distribution has: 1) Random number of trials. 2) Fixed number of successes, in this case 1. f(x) = p(1-p)x-1 where: x = 1, 2, ... , the number of failures until the 1st success. 0 < p < 1, the probability of success.
geometric
When sampling without replacement, the probability of obtaining a certain sample is best given by a
hypergeometric distribution
Excel's HYPGEOM.DIST function can be used to compute _____.
hypergeometric probabilities
To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the
hypergeometric probability distribution.
A probability distribution of a discrete random variable can be: A ____ of the possible values along with their probabilities. A ________ that is used to calculate the probability in response to an input of the random variable's value.
list, formula
The _______ distribution is a discrete probability distribution that applies to the number of occurrences of some event over a specified interval.
poisson
For a discrete random variable X with possible values x1, x2,..., xn, a ______ ______ _______ is a function such that: 1) f(xi) >= 0 2) sum of f(xi) = 1 3) f(xi) = P(X = xi)
probability mass function
A numerical description of the outcome of an experiment is called a
random variable
The variance is a measure of dispersion or variability of a random variable. It is a weighted average of the
squared deviations from the mean
The variance is a weighted average of the _____.
squared deviations from the mean
The _______ ________ of the discrete random variable is another measure of the dispersion. It is the square root of the variance. (Same units as mean).
standard deviation
A weighted average of the values of a random variable, where the probability function provides weights, is known as
the expected value.
The probability Pete will catch fish when he goes fishing is .8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. What is the random variable in this experiment?
the number of days out of 3 that Pete catches fish
