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.;

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

the answer is: the length is 5/6 yards.

give me a or a 5 star rating if this is correct!

step-by-step explanation: