Question
Asked Oct 4, 2019
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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.
a. What is the distribution of X? X
U(
b. Suppose that 36 people are surveyed. What is the distribution of a for this
sample? N
c. What is the probability that the average birth month of the 36 people will be
more than 6.6?
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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. a. What is the distribution of X? X U( b. Suppose that 36 people are surveyed. What is the distribution of a for this sample? N c. What is the probability that the average birth month of the 36 people will be more than 6.6?

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Expert Answer

Step 1

According to the provided details, a = 0 and b = 12.

A uniform distribution has an equal probability for all the outcomes of the random variable, that is, it has a constant probability. A continuous uniform distribution is defined over the range, where a is the smallest value and b is the largest value of the distribution. The values, (a, b) are the parameters of the uniform distribution.

Step 2

(a)

Consider, X be the random variable which is uniformly distributed with the parameters a= 0 and b = 12, that is,

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x-U(a.b) X xU(0.12)

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Step 3

(b)

Here, it is provided that the sample size (n) is 36.

The Central Limit Theorem states that if the sample size is greater than or equal to 30, the...

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Where, u is the population mean, o is the population variance and n is the sample size. Here, mean and population variance can be calculated as: a+b Mean (u 2 0 12 2 = 6

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