Question

Dermatologists strongly recommend that people who are exposed to sunlight should either be covered up or put on sunscreen. Suppose that at a Florida condominium pool only a quarter of residents sit around the pool in the sun with no sunscreen.

a. What is the probability that in a random sample of 10 condo residents 3 or fewer have no sunscreen?

b. What is the expected number of residents who do

Answer 1

a) This is a binomial distribution with parameters:

n = 10, p = 0.25

Hence,

P(3 or fewer)

= P(0) + P(1) + P(2) + P(3)

= 0.7759

b) Expected number of people who apply sunscreen = np = 10*0.25 = 2.5

Hence,

Expected number of people who do not apply sunscreen = 10*(1 - 0.25) = 7.5