Use formulas for parameters for binomial distribution. Suppose the YSORT method

Question

Use formulas for parameters for binomial distribution. Suppose the YSORT method for gender selection is used. Among 875 births, 347 boys were born. Assume having a boy or girl per birth is equally likely.

A) Find the expected number (the mean) of boys. Then find the standard deviation.

B) Use the range rule of thumb to determine the minimum and maximum number of boys.

C) is 347 boys out of 875 births an unusual result? Justify the answer.

For A and B can someone please show me how you go about getting the answers for those two using the formulas? Thank you.

Explanation / Answer

Let X be the random variable that number of boys.

Here X ~Binomial(n = 347, p = 1/2)

where n and are parameters of the Binomial distribution.

A) Find the expected number (the mean) of boys. Then find the standard deviation.

For Binomial distribution :

mean = n*p= 347*1/2 = 173.5

standard deviation = sqrt(n*p*q) = sqrt(347*1/2*1/2)= 9.31

where q = 1-p = 1-1/2 = 1/2

B) Use the range rule of thumb to determine the minimum and maximum number of boys.

The Range Rule of Thumb says that the range is about four times the standard deviation.

s = R/4

9.31 = R/4

R = 37.26

R = maximum -minimum = 37.26

C) is 347 boys out of 875 births an unusual result? Justify the answer.

probability of boys births = 347/875 = 0.40 > 0.05

An observation is said to be unuual iff probability <0.05

It is an usual observation.

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