Question

The Conference Board published information on why companies expect to increase the number of part-time jobs and reduce full-time positions. Eighty-one percent of the companies said the reason was to get a flexible workforce. Suppose 200 companies that expect to increase the number of part-time jobs and reduce full-time positions are identified and contacted.

(a) What is the expected number of these companies that would agree that the reason is to get a flexible workforce?

(b) What is the probability that between 150 and 155 (not including the 150 or the 155) would give that reason?

(c) What is the probability that more than 158 would give that reason?

(d) What is the probability that fewer than 144 would give that reason? *(Round your answer to 2 decimal places.) **(Round z values and ? values to 2 places. Round your answer to 4 decimal places.) (a) expected number = * (b) P(150 < x < 155) = ** (c) P(x > 158) = ** (d) P(x < 144) = **

Answer 1

n = 200

p = 0.81

= n * p = 200 * 0.81 = 162

= sqrt(np(1 - p)) = sqrt(200 * 0.81 * (1 - 0.81))

                              = 5.55

a) Expected number = n * p = 200 * 81 = 162

b) P(150 < X < 155)

= P(151 < X < 154)

= P((150.5 < X < 154.5)

= P((150.5 - )/< (X - )/< (154.5 - )/)

= P((150.5 - 162)/5.55 < Z < (154.5 - 162)/5.55)

= P(-2.07 < Z < -1.35)

= P(Z < -1.35) - P(Z < -2.07)

= 0.0885 - 0.0192

= 0.0693

c) P(X > 158)

= P(X > 159)

= P((X - )/> (158.5 - )/)

= P(Z > (158.5 - 162)/5.55)

= P(Z > -0.63)

= 1 - P(Z < -0.63)

= 1 - 0.2643

= 0.7357

d) P(X < 144)

= P(X < 143)

= P(X < 143.5)

= P((X - )/< (143.5 - )/)

= P(Z < (143.5 - 162)/5.55)

= P(Z < -3.33)

= 0.0004