Question

7.)

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.

1. What is the distribution of XX? XX ~ U( , )
2. Suppose that 38 people are surveyed. What is the distribution of ¯xx¯ for this sample? ¯xx¯ ~ N( , )
3. What is the probability that the average birth month of the 38 people will be more than 4.8?

Answer 1

Answer:

a)

Given,

X ~ Uniform[0 , 12]

b)

Mean = (a + b) / 2

substitute values

= (0 + 12) / 2

= 6

Standard deviation = = (b - a) / sqrt(12)

substitute values

= (12 - 0)/sqrt(12)

= sqrt(12)

= 3.464

x = /sqrt(n)

substitute values

= 3.464/sqrt(38)

= 0.5619

xbar ~ Normal(6 , 0.5619)

c)

P(Xbar > 4.8) = P(z > (4.8 - 6)/0.5619)

= P(z > - 2.14)

= 0.9838226 [since from z table]

= 0.9838