Question

Suppose that a poll taken 10 years ago found that 55​% of parents spank their children. Suppose a recent poll of 500 adults with children finds that 242 indicated that they spank their children. Complete parts​ (a) and​ (b) below. ​(a) Assuming​ parents' attitude toward spanking has not changed since the original​ poll, how many of the 500 parents surveyed would be expected to spank their​ children?

Answer 1

Answer:

Of the 500 parents surveyed 275 would be expected to spank their​ children.

Step-by-step explanation:

Let the random variable X represent the number of parents who spank their children.

It is provided that, from previous studies, p = 55​% of parents spank their children.

A random sample of n = 500 adults were selected.

The event whether a parent spank their children is independent of other parents.

The random variable X thus follows a Binomial distribution with parameters n = 500 and p = 0.55.

The expected value of a Binomial random variable is:

$E(X)=np$

         $=500\times 0.55\\=275$

Thus, of the 500 parents surveyed 275 would be expected to spank their​ children.