Business Stats Test 2 Melvin KK
The "Top Three" at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many "Top Three" outcomes are there?
720
The expected value for a binomial probability distribution is _____.
E(x) = np
Assign prob relative frequency
F/N long run probabilities
For a standard normal distribution, the probability of z ≤ 0 is _____.
For a standard normal distribution, the probability of z ≤ 0 is _____.
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
In a binomial experiment, the probability of success is .06. What is the probability of two successes in seven trials?
.0554
Assign Prob Subjective Method
experience or intuition (educated guess) assign your own probabilities
he 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
The standard deviation of a binomial distribution is _____.
the positive square root of the variance
The collection of all possible sample points in an experiment is _____.
the sample space
examples of an experiement (must list all possible outcomes)
toss a coin, select a random part for inspection conduct a sales call, rolla dice, play a win/loss game
key words for probability
uncertainty, chances, likelihood, likely, chance
U means
union or join together
About 95.4% of the values of a normal random variable are within approximately how many standard deviations of its mean?
±2
The sample mean is the point estimator of _____.
μ
The sample statistic s is the point estimator of _____.
σ
counting rules permutation (special application of multiplication rule)
# of ways to arrange(order) r out of n items n=4 and n=2, 4P2=4!/(4-2)!=12 with calculator, 4-prb-npr-2=12 exp finals 100m sprint, n=8 and r=3=336
counting rules combination
# of ways to select(choose) r out of n items unique groups, removes duplicate ordering n=4,r=2, 4C2=4!/2!(4-2)! with calculator, 4-prb-ncr-2=6 exp 100m sprint, top 3 move on, n=8, r=3 8C3=56
A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is _____.
.0495
A sample of 400 observations will be taken from an infinite population. The population proportion equals .8. The probability that the sample proportion will be greater than 0.83 is _____.
.0668
Assume z is a standard normal random variable. Then P(1.20 ≤ z ≤ 1.85) equals _____.
.0829
An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____.
.100
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below. Number of Breakdowns 0 1 2 3 4 Probability .12 .38 .25 .18 .07 Refer to Exhibit 5-4. The probability of no breakdowns in a month is _____.
.12
If P(A) = .6, P(B) = .3, and P(A ∩ B) = .2, then P(B | A) =_____.
.33
Suppose we flip a fair coin five times and each time it lands heads up. The probability of landing heads up on the next flip is _____.
.5
A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least three spots will be showing up on the die?
.67
If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A ∪ B) = _____.
.68
The following represents the probability distribution for the daily demand of microcomputers at a local store.Demand 1 2 3 4 Probability .1 .2 .3 .2 .2
.7
Suppose x is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is _____.
.9190
A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is _____.
.9511
If P(A) = .38, P(B) = .83, and P(A ∩ B) = .24; then P(A ∪ B) =
.97
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?
.9772
For any continuous random variable, the probability that the random variable takes on exactly a specific value is _____.
0
If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) =
0
Suppose x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is _____.
0
Properties of a Binomial Experiment
1. n identical trials. 2. Each trial can result in only a success or a failure 3. Trials are independent. 4. Probability of a success is constant from trial to trial.
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1401?
1.08
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
Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____.
200 and 2
A sample statistic, such as , that estimates the value of the corresponding population parameter is known as a _____.
A sample statistic, such as , that estimates the value of the corresponding population parameter is known as a _____.
Assume z is a standard normal random variable. Then P(1.41 < z < 2.85) equals _____.
Assume z is a standard normal random variable. Then P(1.41 < z < 2.85) equals _____.
If A and B are independent events with P(A) = 0.1 and P(B) = .4, then _____.
P(A ∩ B) = .04
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. Refer to Exhibit 6-4. What is the random variable in this experiment?
Starting salaries
The number of customers who enter a store during one day is an example of _____.
The number of customers who enter a store during one day is an example of _____.
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.
The standard deviation of a point estimator is the _____.
The standard deviation of a point estimator is the _____.
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.
Event
a collection of sample points
sample point IDEA:assign probability to each outcome
a experimental outcome
sample space
a list of all possible experimental outcomes
A standard normal distribution is a normal distribution with _____.
a mean of 0 and a standard deviation of 1
Variance is _____.
a measure of the dispersion of a random variable
A numerical measure from a population, such as a population mean, is called _____.
a parameter
A numerical measure from a sample, such as a sample mean, is known as _____.
a statistic
Assign Prob Simulation
computing probability with multiple variables Multi-step experiement exp flipping a coin 3 times in a row (tree diagram)
The probability of the intersection of two mutually exclusive events _____.
must always be equal to 0
You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.
mutually exclusive events
A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size _____.
n has the same probability of being selected
As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever _____.
np ≥ 5 and n(1 − p) ≥ 5
As the sample size increases, the ____
standard error of the mean decreases
The standard deviation of is referred to as the _____.
standard error of the proportion
If two events are independent, then _____.
the events have no influence on each other
The sample space refers to _____.
the set of all possible experimental outcomes
The probability of any event is = to
the sum of the probabilities of the sample points in the event
Two events are mutually exclusive if _____.
they have no sample points in common
Larger values of the standard deviation result in a normal curve that is _____.
wider and flatter
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1112?
1.22
Suppose x is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is _____.
.0029
For a standard normal distribution, the probability of obtaining a z value between -2.4 and -2.0 is _____.
.0146
counting rules factoral
# of ways to arrange(order) n items exp ABCD = 24 possible arrangements exp 4, use 4-prb-!=24
A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is _____.
.0228
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below. Number of Breakdowns 0 1 2 3 4 Probability .12 .38 .25 .18 .07
.12
For the standard normal probability distribution, the area to the left of the mean is _____.
0.5
requirements to assign probability
1. let Ei denoth the ith experimental outcome and P(Ei) denote its probability. between o and 1 2. The sum of all probabilities in a sample space must equal 1
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below. Number of Breakdowns 0 1 2 3 4 Probability .12 .38 .25 .18 .07
1.70
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below. Number of Breakdowns 0 1 2 3 4 Probability .12 .38 .25 .18 .07 Refer to Exhibit 5-4. The expected number of machine breakdowns per month is _____.
1.70
A simple random sample of 64 observations was taken from a large population. The population standard deviation is 120. The sample mean was determined to be 320. The standard error of the mean is _____.
15
An experiment consists of tossing four coins successively. The number of sample points in this experiment is _____.
16
Exhibit 5-1The following represents the probability distribution for the daily demand of microcomputers at a local store. Demand 0 1 2 3 4 Probability .1 .2 .3 .4 Refer to Exhibit 5-1. The expected daily demand is _____.
2.2
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
Assign prob Classical method
all outcomes equally likely P(Ei)=1/n exp roll a dice
Any process that generates well-defined outcomes is _____.
an experiment
As the sample size increases, the variability among the sample means _____.
decreases
0------0.5---------1 probability
has to be between 0 and 1
If P(A) = .50, P(B) = .60, and P(A ∩ B) = .30, then events A and B are _____.
independent events
downward upside down U
intersection (overlap)
The symbol ∪ indicates the _____.
intersection of events
The standard deviation of a standard normal distribution _____.
is always equal to 1
The sampling distribution of the sample mean _____.
is the probability distribution showing all possible values of the sample mean
All of the following are true about the standard error of the mean EXCEPT _____.
it is larger than the standard deviation of the population
probabiltiy
likelihood that a particular event will occur
In a standard normal distribution, the range of values of z is from _____.
minus infinity to infinity
Counting Rules - Multiplication
multiply the number of possible outcomes in each step n1=outcomes for step 1 n1*n2*n3=all possible outcomes exp n1=2, n2=2, n3=3 = 8 or use 5 dice 6 sided=6^5=7,776
The purpose of statistical inference is to provide information about the _____.
population based upon information contained in the sample
In a binomial experiment, the _____.
probability of success does not change from trial to trial
experiment
process that generates well-defined outcomes
A numerical description of the outcome of an experiment is called a _____.
random variable
example of an experiment
rolling a 6 sided die
Which of the following is a point estimator?
s
A subset of a population selected to represent the population is a _____.
sample
A probability distribution for all possible values of a sample statistic is known as a _____.
sampling distribution
The probability distribution of all possible values of the sample proportion is the _____.
sampling distribution of
The standard deviation of is referred to as the _____
standard error of the mean
Which of the following is a required condition for a discrete probability function?
∑f(x) = 1