Question

A survey of adults ages 18-29 found that 82% use the Internet. You randomly select 154 adults ages 18-29 and ask them if they use the Internet.

a) Find the probability that exactly 130 people say they use the Internet.

b) Find the probability that at least 130 people say they use the Internet.

c) Find the probability that fewer than 130 people say they use the Internet.

d) Are any of the probabilities in parts (a)-(c) unusual? Explain.

Use a normal approximation to the binomial distribution if possible.

Answer 1

Let X denote the number of people that say they use the Internet

We have :

n = 154

p = 82% = 0.82

a)

Probability that exactly 130 people say they use the Internet = P(X=130)

Using continuity correction,

We use Excel function "NORMSDIST()" as :

Hence,

Probability that exactly 130 people say they use the Internet = 0.0617

b)

Probability that at least 130 people say they use the Internet = P(X 130)

Using continuity correction,

We use Excel function "NORMSDIST()" as :

Hence,

Probability that at least 130 people say they use the Internet = 0.2497

c)

Probability that fewer than 130 people say they use the Internet = P(X<130)

Using continuity correction,

We use Excel function "NORMSDIST()" as :

Hence,

Probability that fewer than 130 people say they use the Internet = 0.7503

d)

Since the probability in part (a) is close to 0 , we can say that probability that exactly 130 people say they use the Internet is unusual.