BANA Exam 2

2.33

Random variable x has the following probability function: f(x)= x/6 for x=1, 2, or 3 What is the expected value of x?

3.05

Roth is a computer-consulting firm. The number of new clients that the firm has 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 Probabiltiy 0 .05 1 .10 2 .15 3 .35 4 .20 5 .10 6 .05 What is the expected number of new clients per month?

2.048

Roth is a computer-consulting firm. The number of new clients that the firm has 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 .05 1 .10 2 .15 3 .35 4 .20 5 .10 6 .05 What is the variance of the number of new clients?

3

Suppose that a basketball player scored, on average, 15 points per game. Also suppose that the distribution of points scored by this player was normal. If he scores 20 points or more 4.78% of the time, what is his standard deviation?

exponential probability distribution

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n):

any numerical value in an interval or collection of intervals

A continuous random variable may assume:

.2150

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?

12,467

A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution?

99.96%

A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. One day he took 15,000 steps. What was his percentage of steps that day?

2.28%

A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. What percent of the time will he exceed 13,000 steps?

expected value

A measure of the average value of a random variable is called a(n):

the number of standard deviations of an observation is below the mean

A negative value of z indicates that:

a standard normal probability distribution

A normal distribution with a mean of zero and a standard deviation of one is called:

2.3

A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let x = the number of puzzles completed successfully by a subject. The psychologist found that x had the following probability distribution: x 1 2 3 4 -------------------------- P(x) .2 .4 .3 .1 What is the mean number of puzzles the subjects can be expected to complete?

continuous random variable

An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:

$350

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)

.4866

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order?

1.5 minutes

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the standard deviation of the distribution?

2.25 minutes

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the standard deviation of the distribution?

f(x)= 2/3e^-2/3x

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their orders at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order?

.3125

Find the probability that a family of five children will have exactly three boys.

is the same for each value of x

For a uniform probability density function, the height of the function:

discrete probability distribution

The Poisson probability distribution is a:

8.1

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?

.1042

The accident rate in a factory is 4 per month. What is the probability that there will be 6 accidents in a particular month?

$23,800

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?

a discrete random variable

The binomial probability distribution is used with:

the mean of the distribution

The center of normal curve is:

np

The expected value for a binomial distribution is:

2.2

The following represents the probability distribution for the daily demand of computer at a local store. Demand Probability 0 .1 1 .2 2 .3 3 .2 4 .2 What is the expected daily demand?

.25

The height of the probability density function for a uniform distribution ranging between 2 and 6 is:

The probability of success changes from trial to trial

The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution:

.6%

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the percentage that, if driven normally, the car will get 100 miles per gallon?

85

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and standard deviation of 10 miles per gallon. What value represents the 50th percentile of this distribution?

.7618

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.

.999995

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 the probability for any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A)=.95, P(B)=.90, P(C)= .99, and P(D)=.90. What is the probability that at least one of the four components will work properly?

P(x) = .40

The probability distribution below represents the random variable, the length of long distance calls in munites in a population. x 5 10 15 20 25 ---------------------------------------- P(x) .1 .2 .3 ? .1 What is the probability that the long distance call last at least 20 minutes?

.60

The random variable x is known to be uniformly distribute between 2 and 12. Compute P(x>6).

7

The random variable x is known to be uniformly distributed between 2 and 12. Compute E(x).

0

The random variable x is known to be uniformly distributed between 2 and 12. Compute P(x=6).

.60

The random variable x is known to be uniformly distributed between 2 and 12. Compute P(x>_ 6).

2.887

The random variable x is known to be uniformly distributed between 2 and 12. Compute the standard deviation of x.

discrete

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 appropriate probability distribution for the random variable is:

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 satisfies the:

.1804

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?

3.5 minutes

The time it takes to ring up a customer at a grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the standard deviation of the distribution?

f(x)=2/7e^-2/7x

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the probability density function for the time it takes to ring up a customer?

.2397

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the probability that it takes more than 5 minutes to ring up a customer?

12.25 minutes

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the variance of this distribution?

(1-e^-2/3.5)-(1-e^-1/3.5)

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. Which of the following expressions gives the probability that it takes from 1 to 2 minutes to ring up a customer?

np(1-p)

The variance Var(x) for the binomial distribution is:

.10567

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?

exponential probability distribution

There is a lower limit but no upper limit for a random variable that follows the:

Hypergeometric probability distribution

To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the:

20

What is the mean of x, given the exponential probability function f(x) = 1/20e^-x/20 for x>_ 0?

Poisson distribution

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a:

I, II, and III

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.

There are exactly two outcomes possible on each trial.

Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?

The number of times a student guesses the answers to questions on a certain test

Which of the following is a discrete random variable?

Ef(x)= 1 for all values of x

Which of the following is a required condition for a discrete probability function?

The trials are dependent upon one another

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

The standard deviation must be one.

Which of the following is not a characteristic of the normal probability distribution?

The graph of the distribution always exhibits symmetry

Which of the following is not true of discrete probability distributions?

When calculating probabilities for discrete distributions, p(x<1) and P(x<-1) will result in the same value

Which of the following statements about discrete distributions is not true?

.1283

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes from 2 to 3 minutes to fill an order?

.50

For the standard normal probability distribution, the area to the left of the mean is:

.0142

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?

exponential probability distribution

If arrival follow a Poisson probability distribution, the time between successive arrivals must follow a(n):

.8220

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?

.87

If z is a standard normal random variable, then compute P(-1.5<z<1.5).

.96

If z is a standard normal random variable, then compute P(z> -1.75).

z=1.75

In a standard normal distribution, what z-score corresponds to the 75th percentile?

$350 and $132.29

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 a standard deviation of $50. What is the expected value and standard deviation, respectively, of the profits that the store makes in a even-day period?

.80

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?