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A budgeting Web site reported that 35​% of U.S. households have withdrawn money from a​ 401(k)...

A budgeting Web site reported that 35​% of U.S. households have withdrawn money from a​ 401(k) or other retirement account for needs other than retirement in 2013. 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 . 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 . 8513. ​(Round to four decimal places as​ needed.) c. What is the probability that more than eight households withdrew funds from a retirement account for needs other than​ retirement? The probability is nothing. ​(Round to four decimal places as​ needed.)

math   Statistics-And-Probability   
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Answer #1

p = 0.35

n = 11

This is a binomial distribution.

P(X = x) = 11Cx * 0.35x * (1 - 0.35)11-x

a) P(X > 8) = P(X = 9) + P(X = 10) + P(X = 11)

                  = 11C9 * 0.359 * 0.852 + 11C10 * 0.3510 * 0.851 + 11C11 * 0.3511 * 0.850

                  = 0.0020 (ans)

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