Question

40% of parents of kindergarteners use time outs as a discipline measure. The experiment is to select 5 parents of kindergarteners at random.

1. What is the probability that none use time outs?
2. What is the probability that at least one uses time outs?
3. What is the probability that at most one uses time outs?
4. What is the mean of this binomial probability function?

Answer 1

Let X be a binomial random variable which denotes the number of parents of kindergartens who use time outs as a discipline measure

Sample size, n = 5

Probability of success, p = 0.4

Thus, q = 1 - p = 0.6

(a) Probability that none use time outs = P(X = 0)

= = = 0.07776

(b) Probability that at least one uses time outs = P(X >= 1)

= 1 - P(X < 1)

= 1 - P(X = 0) = 0.92224

(c) Probability that at most one uses time outs = P(X <= 1)

= P(X = 0) + P(X = 1)

= = 0.33696

(d) Mean of this binomial probability function = np = 2