Question 1

If Z is a standard normal random variable,then P(-1.25 ≤ Z ≤ -0.75)is:

Accepted Answer

A)  0.6678
B)  0.1056
C)  0.2266
D)  0.1210 D

Question 2

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You are the webmaster for your firm's web-site.From your records,you know that the probability that a visitor will buy something from your firm is 0.23.In one day,the number of visitors is 952.
-What is the probability that less than 200 of them will buy something from your firm? Use the normal approximation to the binomial.

Accepted Answer

A)  0.4279
B)  0.5721
C)  0.9279
D)  0.0721 D

Question 3

A normal random variable x has an unknown mean μ and standard deviation σ = 2.5.If the probability that x exceeds 7.5 is 0.8289,find μ.

Accepted Answer

It is given that x is normally distributed with σ = 2.5 but with unknown mean μ,and that P (x > 7.5)= 0.8289.In terms of the standard normal random variable z,we can write P(X > 7.5)= P[Z > (7.5 - μ)/2.5] = 0.8289,Z = -0.95 Since the area to the right of (7.5 - μ)/2.5 is greater than 0.5,then (7.5 - μ)/2.5 must be negative,and that P[(7.5 - μ)/2.5 < z < 0] = 0.3289.Hence,(7.5 - μ)/2.5 = -0.095.This implies μ = 9.875.

Question 4

The normal probabilities are calculated using the table of standard normal distribution where the mean and standard deviations are,respectively:

Accepted Answer

A)  1 and 1.
B)  10 and 0.
C)  0 and 1.
D)  0 and 10.

Question 5

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes.
-Sixty percent of the time,the stoplight will change before you have to wait X seconds,what is the value of X?

Accepted Answer

A)  72 seconds
B)  60 seconds
C)  48 seconds
D)  36 seconds

Question 6

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The continuous random variable X is uniformly distributed over the interval 4 to 10.
-What is the standard deviation of this distribution?

Accepted Answer

A)  1.732
B)  3.162
C)  2.646
D)  2.449

Question 7

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. -Find the 5^th percentile.

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 8

In a recent survey of high school students,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $52.30.Suppose you are told that there is an 80% probability that a randomly-selected student spends somewhere between $49.74 and $54.86.What is the standard deviation of the amount of money spent by high school students monthly?

Accepted Answer

The answer of In a recent survey of high school...

Question 9

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A professor sees students during regular office hours.Times spent with students follow an exponential distribution with mean of 12 minutes.
-Find the probability that a given student spends less than 15 minutes with the professor.

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 10

Checkout times in a grocery store follow the exponential distribution with a mean time of 6.5 minutes.What is the probability that the checkout time (T)for the next customer will be less than 5 minutes?

Accepted Answer

A)  0.537
B)  0.463
C)  0.257
D)  0.950

Question 11

The probability is 0.2 that X is greater than what number?

Accepted Answer

The answer of The probability is 0.2 that X is...

Question 12

We can obtain probabilities for any normally distributed random variable by first converting the random variable to the standard normally distributed random variable.

Accepted Answer

A) True 
 B)False

Question 13

The profit for a production process is equal to $7,200 minus 2.8 times the number of units produced.The mean and variance for the number of units produced are 1,100 and 800,respectively.Find the mean and variance of the profit.

Accepted Answer

The answer of The profit for a production process is...

Question 14

The term used by fund managers to describe the relationships between two stock prices is:

Accepted Answer

A)  speculating.
B)  hedging.
C)  investing.
D)  betting.

Question 15

A catalog company administered a survey to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3.5 minutes.What proportion of customers having to hold more than 5.0 minutes will hang up before placing an order?

Accepted Answer

A)  0.2397
B)  0.5714
C)  0.4286
D)  0.7603

Question 16

In the normal distribution,the curve approaches,but never intercepts the horizontal axis either to the left or right.

Accepted Answer

A) True 
 B)False

Question 17

Any set of normally distributed data can be transformed to a standardized form.

Accepted Answer

A) True 
 B)False

Question 18

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a country club.The number of times you expect to play golf in a month is represented by a random variable with a mean of 10 and a standard deviation of 2.2.Assume you pay monthly membership fees of $500 per month and pay an additional $50 per round of golf.
-What is your average monthly bill from the country club?

Accepted Answer

A)  $700
B)  $800
C)  $900
D)  $1000

Question 19

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.
-What proportion of the total area under the normal curve is above the mean?

Accepted Answer

A)  50%
B)  68%
C)  95%
D)  99.7%

Question 20

The total area under the curve of the probability density function for a continuous random variable depends on the shape of the probability distribution of the random variable.

Accepted Answer

A) True 
 B)False

Exam 5: Continuous Random Variables and Probability Distributions

If Z is a standard normal random variable,then P(-1.25 ≤ Z ≤ -0.75) is:

A normal random variable x has an unknown mean μ and standard deviation σ = 2.5.If the probability that x exceeds 7.5 is 0.8289,find μ.

The normal probabilities are calculated using the table of standard normal distribution where the mean and standard deviations are,respectively:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes. -Sixty percent of the time,the stoplight will change before you have to wait X seconds,what is the value of X?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is the standard deviation of this distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. -Find the 5^th percentile.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A professor sees students during regular office hours.Times spent with students follow an exponential distribution with mean of 12 minutes. -Find the probability that a given student spends less than 15 minutes with the professor.

Checkout times in a grocery store follow the exponential distribution with a mean time of 6.5 minutes.What is the probability that the checkout time (T) for the next customer will be less than 5 minutes?

The probability is 0.2 that X is greater than what number?

We can obtain probabilities for any normally distributed random variable by first converting the random variable to the standard normally distributed random variable.

The profit for a production process is equal to $7,200 minus 2.8 times the number of units produced.The mean and variance for the number of units produced are 1,100 and 800,respectively.Find the mean and variance of the profit.

The term used by fund managers to describe the relationships between two stock prices is:

In the normal distribution,the curve approaches,but never intercepts the horizontal axis either to the left or right.

Any set of normally distributed data can be transformed to a standardized form.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4. -What proportion of the total area under the normal curve is above the mean?

The total area under the curve of the probability density function for a continuous random variable depends on the shape of the probability distribution of the random variable.

Exam 5: Continuous Random Variables and Probability Distributions

If Z is a standard normal random variable,then P(-1.25 ≤ Z ≤ -0.75) is:

A normal random variable x has an unknown mean μ and standard deviation σ = 2.5.If the probability that x exceeds 7.5 is 0.8289,find μ.

The normal probabilities are calculated using the table of standard normal distribution where the mean and standard deviations are,respectively:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes. -Sixty percent of the time,the stoplight will change before you have to wait X seconds,what is the value of X?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is the standard deviation of this distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. -Find the 5th percentile.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A professor sees students during regular office hours.Times spent with students follow an exponential distribution with mean of 12 minutes. -Find the probability that a given student spends less than 15 minutes with the professor.

Checkout times in a grocery store follow the exponential distribution with a mean time of 6.5 minutes.What is the probability that the checkout time (T) for the next customer will be less than 5 minutes?

The probability is 0.2 that X is greater than what number?

We can obtain probabilities for any normally distributed random variable by first converting the random variable to the standard normally distributed random variable.

The profit for a production process is equal to $7,200 minus 2.8 times the number of units produced.The mean and variance for the number of units produced are 1,100 and 800,respectively.Find the mean and variance of the profit.

The term used by fund managers to describe the relationships between two stock prices is:

In the normal distribution,the curve approaches,but never intercepts the horizontal axis either to the left or right.

Any set of normally distributed data can be transformed to a standardized form.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4. -What proportion of the total area under the normal curve is above the mean?

The total area under the curve of the probability density function for a continuous random variable depends on the shape of the probability distribution of the random variable.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. -Find the 5^th percentile.