In a survey, 70% of Americans said they own an answering machine. If 5 Americans are selected at random:

a. Find the probability that exactly 3 own an answering machine;

b. Find the mean number of people who own an answering machine.;

B. find the mean number of people who own one

Step-by-step explanation:

We would assume a binomial distribution for the Americans that own answering machines. The formula is expressed as

P (x = r) = nCr * p^r * q^ (n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 70% = 70/100 = 0.7

q = 1 - p = 1 - 0.7

q = 0.3

n = 5

x = r = 3

Therefore,

P (x = 3) = 5C3 * 0.7^3 * 0.3^ (5 - 3)

P (x = 3) = 10 * 0.343 * 0.09

P (x = 3) = 0.3087

b) mean = np = 5 * 0.7 = 3.5