Question

Under ordinary circumstances: For all babies born in the entire global population, the proportion of male births tends to be consistently a bit higher, than the proportion of female births (Source: WHO - World Health Organization).

In fact: For a randomly sampled individual birth from the global population, the probability that the baby's sex will be male is approximately 51.22%.

Imagine that we will randomly record the sex outcome at birth for 25 future individual babies from the global population.

We will let random variable X stand for the total number of male births in our sample.

In this scenario, what is the numerical value of E(X)?

Round to one digit past the decimal point, and state just the number part of your answer (no units).

In this same scenario:

What is the numerical value of SD(X)?

Round to one digit past the decimal point, and state just the number part of your answer (no units).

In this same scenario:

What is the approximate value of P(X≤11) ?

Write your answer as a percentage value, and round to three digits after the decimal point. Include a percent symbol after your answer (no spaces).

In this same scenario:

What is the approximate value of P(X>11) ?

Write your answer as a percentage value, and round to three digits after the decimal point. Include a percent symbol after your answer (no spaces).

Answer 1

Here X has binomial distribution with following parameters

n=25 and p=0.5122

The numerical value of E(X) is

The numerical value of SD(X) is

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Using continuity correction factor is

Answer : In requied form 30.153%

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Using continuity correction factor is

Answer : In requied form 69.847%