Question

6-8. Only five percent of people who lose weight keep it off. Consider 20 people selected at random who lost weight. 6. What is the chance none of those people who lost weight kept it off? 7. What is the chance more than 3 of the 20 people who lost weight kept it off? 8. If one were to look at a large number of groups of 20 people who lost weight, how many in the average group would have lose weight and kept it off?

Answer 1

This is binomial prbability
As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

Here p = 0.05 and n = 20

6.
P(X=0) = 20C0 * 0.05^0 * (1-0.05)^(20-0) = 0.3585

7.
P(X > 3) = 1 - P(X < 4)
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= 0.3585 + 0.3774 + 0.1887 + 0.0596
= 0.9841

P(X > 3) = 1 - 0.9841 = 0.0159

8.
Average = 0.05*20 = 1