Forty 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.

Let X be the event of feeling secure after saving $50,000,

Given,

The probability of feeling secure after saving $50,000, p = 40 % = 0.4,

So, the probability of not  feeling secure after saving $50,000, q = 1 - p = 0.6,

Since, the binomial distribution formula,

Where,

If 8 households choose randomly,

That is, n = 8

(a) the probability of the number that say they would feel secure is exactly 5

(b) the probability of the number that say they would feel secure is more than five

(c) the probability of the number that say they would feel secure is at most five

step-by-step explanation: