Question

In: Statistics and Probability

The Smith family was one of the first to come to the U.S. They had 9...

The Smith family was one of the first to come to the U.S. They had 9 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had: at least 8 girls? at most 7 girls?

Expert Solution

Solution:

Given:

The Smith family was one of the first to come to the U.S. They had 9 children.

Thus Sample size = n = 9

p = the probability of a child being a girl = 0.5

thus q = 1 - p = 1 - 0.5 = 0.5

Part a) Find the probability that the Smith family had at least 8 girls.

That is find:

Here X = Number of girls follows a Binomial distribution with parameters n = 9 and p = 0.5

Thus using binomial probability distribution, we get:

where

Thus

and

Thus

Thus the probability that the Smith family had at least 8 girls is

Part b) Find the probability that the Smith family had at most 7 girls.

That is:

the probability that the Smith family had at most 7 girls is .

orchestra answered 2 years ago

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