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.2.17-T A budgeting Web site reported that 35% of US households have withdrawn m

ID: 3075172 • Letter: #

Question

.2.17-T A budgeting Web site reported that 35% of US households have withdrawn money from a 401(k) or other retirement account for needs ot A random sample of 11 U.S. households was selected. Complete parts a through e below a. What is the probability that exactly four households withdrew funds from a retirement account for needs other than retirement? The probability is 0.2428 Round to four decimal places as needed.) b. What is the probability that less than six households withdrew funds from a retirement account for needs other than retirement? The probability is Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer remaining

Explanation / Answer

Probability that a random household has withdrawn money = 0.35
a)
Let X be the random variable denoting the number of household who withdrew money.
Probability that 4 out of 11 households withdrew money = P(X = 4)
= 11C4 (0.35)4(1-0.35)7 = 0.2428
b)
Probability that < 6 households withdrew money = P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
P(X = 0) = 11C0 (0.35)0(1-0.35)11 = 0.0088
P(X = 1) = 11C1 (0.35)1(1-0.35)10 = 0.0518
P(X = 2) = 11C2 (0.35)2(1-0.35)9 = 0.1395
P(X = 3) = 11C3 (0.35)3(1-0.35)8 = 0.2254
P(X = 4) = 11C4 (0.35)4(1-0.35)7 = 0.2428
P(X = 5) = 11C5 (0.35)5(1-0.35)6 = 0.1830
P(X < 6) = 0.0088 + 0.0518 + 0.1395 + 0.2254 + 0.2428 + 0.1830 = 0.8513