50 percent of households say they would feel secure if they had 50000 in savings

Question

50 percent of households say they would feel secure if they had 50000 in savings. You randomly select 8 households and ask them if they would feel secure if they had 50000 in savings. Find the probability that the number that say tgry would feel secure is A) exactly 5 B)more than 5 And c) at most 5 50 percent of households say they would feel secure if they had 50000 in savings. You randomly select 8 households and ask them if they would feel secure if they had 50000 in savings. Find the probability that the number that say tgry would feel secure is A) exactly 5 B)more than 5 And c) at most 5 Find the probability that the number that say tgry would feel secure is A) exactly 5 B)more than 5 And c) at most 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 = 0.855

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