Question

A recent survey found out that 52% of girls 14-17 years old wear contacts. We take a random sample of 20 girls 14-17 years old.

a) Is this a binomial distribution? why or why not?
b) Find the probability that exactly 15 girls in our sample of 20 are wearing contacts.
c) Find the probability that at least 10 girls are wearing contacts"

Answer 1

Yes, this is a binomial distribution because there are a fixed number of trials and each trial has two possible outcomes.

Why is this a binomial distribution?

The distribution is a binomial distribution because it meets the following conditions:

(i) There is a fixed number of trials (n = 20).

(ii) Each trial has two possible outcomes (wearing contacts or not wearing contacts).

(iii) The probability of success (wearing contacts) is p = 0.52.

(iv) The trials are independent.

b) the probability that exactly 15 girls in our sample of 20 are wearing contacts.

p = (15, 20, 0.52)

0.02171201353785329

The probability that exactly 15 girls in our sample of 20 are wearing contacts is 0.0217.

c) the probability that at least 10 girls are wearing contacts.

p = 1 - (9, 20, 0.52)

0.6568408734228279

The probability that at least 10 girls are wearing contacts is 0.6568.