Got some things wrong, correct answers are shown. Can you help me? Showing work

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Got some things wrong, correct answers are shown. Can you help me? Showing work would be preferred.

A poll found that 30% of adults do not work at all while on summer vacation. In a random sample of 9 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 working during summer vacation Adults not working during summer vacation b. Explain why x is (approximately) a binomial random variable. Choose the correct answer below. ( A. The trials are not independent. O B The experiment consists of only identical trials. 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. There are three possible outcomes on each trial c. Give the value of p for this binomial experiment. p= .30 d. Find P(x 3) Px-3)-0 2668 (Round to ftour decimal places as needed.) e. Find the probability that 2 or fewer of the 9 adults do not work during summer vacation. Pixs2)-0.4628 (Round to four decimal places as needed.)

Explanation / Answer

a) X represents the number who do not working during summer vacation and therefore is considered a success event.

Answer: Adults not working during summer vacation

d) P(X = 3) = nck * pk * (1-p)(n-k) = 9c3 * 0.33 * 0.76 = 0.2668

e) P(X <= 2) = P(X = 0) + P(X = 1) + P(X=2) = 9c0 * 0.30 * 0.79 + 9c1 * 0.31 * 0.78 + 9c2 * 0.32 * 0.77 = 0.4628

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