12 of 14 (0 complete) This Test: 14 pts possi stion: 1 pt Thirty percent of hous

Question

12 of 14 (0 complete) This Test: 14 pts possi stion: 1 pt 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. P(5) (Round to three decimal places as needed.) (b) Find the probability that the number that say they would feel secure is more than five. (Round to three decimal places as needed.) (c) Find the probability that the number that say they would feel secure is at most five. Round to three decimal places as needed.)

Explanation / Answer

Solution:-

p = 0.30

n = 8

a) The probability that the number that say they would feel secure is exactly five is 0.0467.

x = 5, n = 8

By applying binomial distribution

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

P(5) = 0.0467

b) The probability that the number that say they would feel secure is more than five is 0.0113.

x = 5, n = 8

By applying binomial distribution

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

P(x > 5) = 0.0113

c) The probability that the number that say they would feel secure is atmost five is 0.9887.

x = 5, n = 8

By applying binomial distribution

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

P(x < 5) = 0.9887

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