Question

For each probability and percentile problem, draw the picture. Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks).

part G: Enter an exact number as an integer, fraction, or decimal. P(2 < x < 9) =

Part H: Find the probability that a person is born after week 42. (Enter an exact number as an integer, fraction, or decimal.)

Part I: Enter an exact number as an integer, fraction, or decimal. P(13 < x | x < 29) =

Answer 1

Answer:

According to the given question , Births are approximately distributed uniformly from one to 53 (spread of 52 weeks), therefore, the uniform distribution (probability density function is written as:

when

   otherwise

As and , then the pdf of this uniform distribution is:

Diagram of this distribution is:

The mean and standard deviation of an uniform distribution is as follows:

and

(i) The probability of

We can solve this by the following way:

step-I: The probability density function of

step-II: Therefore the required probability is :

  

  

diagram:

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