1. A computer selects a number XX from 0 to

1.  

 A computer selects a number XX from 0 to 7 randomly and uniformly. Round all answers to 4 decimal places where possible.

a. What is the distribution of XX? XX ~ U(,)

b. Suppose that the computer randomly picks 38 such numbers.  What is the distribution of ¯xx¯ for this selection of numbers. ¯xx¯ ~ N(,)

c. What is the probability that the average of 38 numbers will be less than 3.8? 

2. 

 

Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible.

a. What is the distribution of XX? XX ~ U(,)

b. Suppose that 37 people are surveyed.  What is the distribution of ¯xx¯ for this sample? ¯xx¯ ~ N(,)

c. What is the probability that the average birth month of the 37 people will be less than 4.8? 

3.  

Suppose that the age of students at George Washington Elementary school is uniformly distributed between 6 and 11 years old. 42 randomly selected children from the school are asked their age. Round all answers to 4 decimal places where possible.

a. What is the distribution of XX? XX ~ U(,)

Suppose that 42 children from the school are surveyed. Then the sampling distribution is

b. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)

c. What is the probability that the average of 42 children will be between 8 and 8.4 years old? 

4.  

The number of seconds XX after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible.

  1. What is the distribution of XX? XX ~ U(,)

 then the sampling distribution is

a. Suppose that 36 classes are clocked.  What is the distribution of ¯xx¯ for this group of classes? ¯xx¯ ~ N(,)

b. What is the probability that the average of 36 classes will end with the second hand between 26 and 35 seconds? 

 

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