Question

In February 2007, the MITI Poll surveyed adults living in Canada. When asked about the current state of the job market, 45% indicated that nw is a good time to be looking for a quality job. The reminder answered no opinion or that now is a bad time to be looking for a quality job. The results were more positive than survey taken in 2003, but down from the boom years of the 1990s. Suppose that you select a random sample of 10 adults and survey them concerning the current status of the job market. Assume that 45% of the adults in Canada still think that now is a "good time" to be looking for a quality job and further assume that the number of the 10 adults thinking that now is a "good time' is distributed as a binominal random variable.

a. What is the mean and the standard deviation of this distribution?

b. What is the probability that exactly three think that now is a "good time"?

c. What is the probability that three or less think that now is a "good time"?

Answer 1

Let X be a binomial random variable which denotes the number of adults(out of 10 adults) who think that now is a "good time"

Sample size, n = 10

Probability of success, p = 0.45

Thus, q = 1 - p = 0.55

(Success is the event that the adult think that now is a "good time"

(a) Mean of X = np = 10 * 0.45 = 4.5

Standard deviation of X =
(npg (npq) V
=
/(10 0.45 0.55)
= 1.573

(b) Required probability = P(X = 3)

=

(10 0.45 0.55

= 0.1665

(c) Required probability = P(X <= 3)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

=

10 10 *0.45 0.55 1 10 0.4520.553 2 -10 3 0.55+ 0.45*0,55

= 0.266