Fifty percent of households say they would feel secure if they had $50,000 in sa
ID: 3262772 • Letter: F
Question
Fifty 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) = (b) Find the probability that the number that say they would feel secure is more than five. P(x > 5) = (c) Find the probability that the number that say they would feel secure is at most five. P(x lessthanorequalto 5) =Explanation / Answer
p = 0.5
n = 8
P(X = x) = 8Cx * 0.5x * (1-0.5)8-x
A) P(X = 5) = 8C5 * 0.55 * 0.53 = 0.219
B) P(X > 5) = P(X = 6) + P(X = 7) + P(X = 8)
= 8C6 * 0.56 * 0.52 + 8C7 * 0.57 * 0.51 + 8C8 * 0.58 * 0.50
= 0.145
C) P(X < 5) = 1 - P(X > 5) = 1 - 0.145 = 0.856
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