Sixty dash fivesixty-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.

To solve the following problems, we use the binomial probability equation:

P (r) = [n! / (n-r) ! r!] p^r q^ (n-r)

where,

n = total number of households = 8

r = number of sample

p = probability of success = 65% = 0.65

q = probability of failure = 0.35

A. r = 5

P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3

P (r=5) = 0.28

B. r >5

P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2

P (r=6) = 0.26

P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1

P (r=7) = 0.14

P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0

P (r=8) = 0.03

Therefore total is:

P (r>5) = 0.26 + 0.14 + 0.03 = 0.43

C. r ≤ 5

P (r ≤ 5) = 1 - P (r>5)

P (r ≤ 5) = 1 - 0.43

P (r ≤ 5) = 0.57