Question

The probability that an at home pregnancy test will correctly identify a pregnancy is 0.91. Suppose 18 randomly selected pregnant women with typical hormone levels are each given the test.

Rounding your answer to four decimal places, find the probability that

Answer 1

This is the case of a Binomial distribution, with the following parameters:

n = 18, p = 0.91

Let X denote the random variable which counts the number of women who correctly identify pregnency using the test.

The pdf for this distribution is:

P(X=x) = ⁿC_x*(p^x)*((1-p)^(n-x))

So for this case we have:

P(X=x) = ¹⁸C_x*(0.91^x)*(0.09^(18-x))

Let's suppose you want to find the probability that exactly 15 women are able to correctly identify pregnency.

So this means we want to find P(X = 15)

Solving we get:

P(X=15) = ¹⁸C₁₅*(0.91^15)*(0.09^(18-15)) = 0.144

In this way you can calculate many other kinds of probabilities as you desire.