W3: MyStatlab Quizzes & X i Secure I https://upperiowa.brightspace.com/d2/le/con

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W3: MyStatlab Quizzes & X i Secure I https://upperiowa.brightspace.com/d2/le/content/50378/viewContent/476460/View Score: 0 of 1 pt 7 of 11 (6 complete) HW Score: 38.64%, 425 of 11 pts 4.2.19 Thirty percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five (a) Find the probability that the number that say they would feel secure is exactly five. Round to three decimal places as needed )

Explanation / Answer

This is binomial probability problem

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

here p = 0.3 and n = 8

a)
P(X = 5) = 8C5 * 0.3^5 * (1-0.3)^(8-5) = 0.0467

b)
P(X > 5) = P(X = 6) + P(X = 7) + P(X = 8)

P(X = 6) = 8C6 * 0.3^6 * (1-0.3)^(8-6) = 0.010
P(X = 7) = 8C7 * 0.3^7 * (1-0.3)^(8-7) = 0.00122
P(X = 8) = 8C8 * 0.3^8 * (1-0.3)^(8-8) = 0.00007

P(X > 5) = 0.0113

c)
P(X <= 5) = 1 - P(X > 5)
P(X <= 5) = 1 - 0.0113 = 0.9887

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