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?
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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.
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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?
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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.
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?
