Question

Births are approximately uniformly distributed between 52 weeks of the year. They can be said to follow a uniform distribution form 1 to 53 . Round answers up to 4 decimal places when possible.

The probability that a person will be born between weeks and 40 is P(15<x <40) =____

The probability that a person will be born after week 15 is P (x>15) = ______

f P (x>10|x<17)= ______

Step 1

Given births are uniformly distributed between 1 to 53 weeks.

a = 1 and b = 52.

The probability distribution of a uniform distribution is 1/(b-a) = 1/(53-1) = 1/52

The probability that a person born between 15 and 40 weeks is given by the area under the distribution curve between 15 and 40.

We see that the area between 15 and 40 under probability distribution is rectangle with length =(40-15) = 25 breadth = 1/52.

Area = length*breadth = 25*(1/52) = 0.4808

Step 2

The probability that a person born after 15 weeks is the area under the probabilit curve from 15 to 53 a shown in figure.

The area ...

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