statistics multiple variations

Question

Births are approximately Uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimal places when possible.

1. 1)  The mean of this distribution is :
2. 2)   The standard deviation is :
3. 3)   The probability that a person will be born at the exact moment that week 47 begins is        P(x = 47) = 
4. 4)   The probability that a person will be born between weeks 7 and 26 is  = 
5. 5)   The probability that a person will be born after week 39 is P(x > 39) = 
6.        P(x > 3 | x < 8) = 
7. 6)   Find the 57th percentile. 
8. 7)   Find the minimum for the upper quartile. 

Answer 1

1. 1) The mean of this distribution is : (b+a)/2 = (53+1)/2 = 27
2. 2)  The standard deviation is : sqrt((b-a)^2/12)=sqrt((53-1)^2/12) = 15.01
3. 3)  The probability that a person will be born at the exact moment that week 47 begins is    P(x = 47) = 0
4. 4)  The probability that a person will be born between weeks 7 and 26 is P(7<x<26) = (26-7)*(1/52) = 0.37
5. 5)  The probability that a person will be born after week 39 is P(x > 39) = (53-39)*(1/52) = 0.27
6.     P(x > 3 | x < 8) = P(X>3 and X<8 )/ P(X<8) = (5/52) / (7/52) = 0.71
7. 6)  Find the 57th percentile. 0.57 = (X-1)/52 -> X=(0.57*52)+1 = 30.64
8. 7)  Find the minimum for the upper quartile. (0.75*52)+1 = 40