Question

Seventy dash fiveSeventy-five percent of households say they would feel secure if they had​ $50,000 in savings. You randomly select 88 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.

Answer 1

A) 0.2076
B) 0.6786
C) 0.3214

Explanation:
A) $P(X=5)=_8C_5(0.75)^5 \times(1-0.75)^{8-5} \\ \\=_8C_5(0.75)^5 \times (0.25)^3=0.2076$
B) We find the probability that X=6, 7, or 8:
$P(X=6)=_8C_6(0.75)^6(0.25)^2=0.3115 \\ \\P(X=7)=_8C_7(0.75)^7(0.25)^1=0.267 \\ \\P(X=8)=_8C_8(0.75)^8(0.25)^0=0.1001 \\ \\0.3115+0.267+0.1001=0.6786$
C) P(X≤5) = 1-P(X>5) = 1-0.6786 = 0.3214