Question

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. What is the distribution of X ? X ~ U( , ) Suppose that 36 people are surveyed. What is the distribution of ¯ x for this sample? ¯ x ~ N( , ) What is the probability that the average birth month of the 36 people will be more than 4.7?

Answer 1

Solution:

1)

distribution of X ~ U(0,12)

2)

mean μ=(a+b)/2 =	6
varaince =σ2= (b-a)2/12 =	12.0000
standard deviation σ=(b-a)/√12=	3.4641

std error=σx̅=σ/√n=3.4641/√36 =

0.5773

distribution of x ¯ ~ N(6, 3.4641)

3)

probability =P(X<4.7)=(Z<(4.7-6)/0.5773)=P(Z<-2.25)=0.01222

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