Question

Fifty-two percent of adults admit that chocolate chip is their favorite cookie. You randomly select 89 adults and ask each if chocolate chip is their favorite kind of cookie. What is the probability that more than 55 admit that chocolate chip is their favorite kind of cookie?

Answer 1

Let the random variable X represent the number of people among the selected 89 adults who admit that chocolate chip is their favorite cookie. We will do this problem using two different methods.

First Method : Using Binomial Distribution

This will give a more exact answer. Clearly X will have a binomial distribution with N = 89 and p = 0.52. We need to find the probability of P(X>55). The probability distribution function for a binomial random variable is given as,

Hence the probability required in this case would be given by,

Second method : Approximation as a normal distribution

Since the sample size is large we can approximate X as a normal distribution. The mean of the distribution would be given by,

The standard deviation of the distribution would be given by,

Now the required probability would be given by,