# 1.suppose you have a random variable that is uniformly distributed

1.Suppose you have a random variable that is uniformly distributed between 3 and 27.  What is the expected value for this random variable? Answer to one decimal place if necessary.

2.Suppose you have a random variable that is uniformly distributed between 125 and 176.  What is the expected value for this random variable? Answer to one decimal place if necessary.

3.Suppose you have a random variable that is uniformly distributed between 35 and 62.  What is the variance for this random variable? Answer to one decimal place if necessary.

4.Suppose you have a random variable that is uniformly distributed between 71 and 652.  What is the probability of observing a random draw greater than or equal to 379? Answer to three decimal place if necessary.

5.Suppose you have a random variable that is uniformly distributed between 0 and 2.  What is the probability of observing a random draw greater than or equal to 0.19? Answer to three decimal place if necessary.

6.An Italian restaurant advertises that carryout orders take about 22 minutes.  Assume that the time it takes for an order to be ready follows the exponential distribution with a mean of 22.  What is the probability that an order will be ready within 17 minutes?  Answer to three decimal places if needed.

7.A Thai restaurant advertises that carryout orders take about 20 minutes.  Assume that the time it takes for an order to be ready follows the exponential distribution with a mean of 20.  What is the probability that an order will take longer than 28 minutes?  Answer to three decimal places if needed.

8.Suppose that the weight of cereal in a box is normally distributed around a mean of 20, measured in ounces, with a standard deviation of 0.17.  What is the z value for a box with 19.86 ounces of cereal?  Answer to three decimal places if needed.

9.Suppose that the weight of cereal in a box is normally distributed around a mean of 15, measured in ounces, with a standard deviation of 0.02.  What is the z value for a box with 15.18 ounces of cereal?  Answer to three decimal places if needed

10.Suppose that the loan amount on mortgages for a particular zip code is normally distributed with a mean of 153,453, measured in dollars, with a standard deviation of 12,114.  What is the z value for a loan of 176,575 dollars?  Answer to three decimal places if needed.

11.Suppose that the auto loans from a bank are normally distributed with a mean of \$23,334 and a standard deviation of 3,412.  What is the probability that a randomly selected loan will be for more than \$23,334? Answer to three decimal places if necessary.

12.Suppose that the auto loans from a bank are normally distributed with a mean of \$23,334 and a standard deviation of 3,412.  What is the probability that a randomly selected loan will be for more than \$25,000?  Answer to three decimal places if necessary.

13.Suppose that the auto loans from a bank are normally distributed with a mean of \$23,334 and a standard deviation of 3,412.  What is the probability that a randomly selected loan will be for less than \$26,000?  Answer to three decimal places if necessary.

14.A uniformly distributed random variable

must be discrete.

must be between 0 and 1.

has the same density for all possible values that the random variable can take on.

has a variance equal to the mean.

15.The number of cars that a family owns is a continuous variable.

True

False

16.The total amount a cereal company spends on payroll is a continuous variable.

True

False

17.The average of 2, 4, 6 is

1

2

3

4

18.The minimum of 2, 4, 6 is

1

2

3

4

19.For the exponential distribution the mean and standard deviation are

the same.

unrelated.

related by the square root function.

related by the exponential pdf.

20.The ________ distribution has the following CDF: 1-exp(-x/μ).  Use all lower case letters and double check your spelling exponential

21.The exponential distribution is symmetric.

True

False

22.For the normal distribution the mean and variance are

the same.

unrelated.

related by the square root function.

related by the normal pdf.

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