Question

A poll found that 35 ?% of adults do not work at all while on summer vacation. In a random sample of 10 ?adults, let x represent the number who do not work during summer vacation. Complete parts a through e.

a. For this? experiment, define the event that represents a? "success." Choose the correct answer below. Adults not working during summer vacation Adults working during summer vacation b. Explain why x is? (approximately) a binomial random variable. Choose the correct answer below.

A. There are three possible outcomes on each trial.

B. The trials are not independent.

C. The experiment consists of identical? trials, there are only two possible outcomes on each trial? (works or does not? work), and the trials are independent.

D. The experiment consists of only identical trials. c. Give the value of p for this binomial experiment. pequals nothing d. Find ?P(xequals 3 ?). ?P(xequals 3?)equalsnothing ?(Round to four decimal places as? needed.) e. Find the probability that 2 or fewer of the 10 adults do not work during summer vacation. ?P(xless than or equals 2?)equalsnothing ?(Round to four decimal places as? needed.)

Answer 1

a) The event that the Adults not working during summer vacation represents a success.

b) The experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent. Hence x is a binomial random variable.

c) Here the probability of success is p=0.35

d)

### By using R command:

> dbinom(3,10,0.35)
[1] 0.2522196

e) The probability that 2 or fewer of the 10 adults do not work during summer vacation is given by:

### By using R command:

> pbinom(2,10,0.35)
[1] 0.2616074