PLEASE DOUBLE CHECK This Question: 6 pts 17 of 19 (7 complete) This Test: 30 pts

Question

PLEASE DOUBLE CHECK

This Question: 6 pts 17 of 19 (7 complete) This Test: 30 pts possible Question Help * A recent study found that 57% of workers between the ages of 20-29 cash out their retirement accounts when they lose their obs or move to a new employer. Complete parts a through e below based on a random sample of14 workers between the ages of 20-29 who lost their jobs or changed employens a. What is the probability that exactly 5 workers cashed out their retirement accounts? The probability is Round to four decimal places as needed.) b. What is the probability that all 14 workers from the sample cashed out their retirement accounts? The probability is Round to four decimal places as needed) c. What is the probability that 11 or fewer workers cashed out their retirement accounts? The probability is Round to four decimal places as needed.) d. What are the mean and standard deviation for this distribution? The mean is Type an integer or a decimal.) The standard deviation is Round to four decimal places as needed) Click to select your answer(s). 247 PM Type here to search

Explanation / Answer

p = 0.57

n = 14

P(X = x) = nCx * px * (1 - p)n - x

a) P(X = 5) = 14C5 * (0.57)^5 * (0.43)^9 = 0.0605

b) P(X = 14) = 14C14 * (0.57)^14 * (0.43)^0 = 0.0004

c) P(X < 11) = 1 - P(X > 11)

                    = 1 - P((X = 12) + P(X = 13) + P(X = 14))

                     = 1 - ( 14C12 * (0.57)^12 * (0.43)^2 + 14C13 * (0.57)^13 * (0.43)^1 + 14C14 * (0.57)^14 * (0.43)^0)

                     = 0.9758

d) mean = n * p = 14 * 0.57 = 7.98

standard deviation = sqrt(n * p * (1 - p))

                                = sqrt(14 * 0.57 * 0.43) = 1.8524

e) Option - C

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