Five percent of workers in a city use public transportation to get to work. A tr

Question

Five percent of workers in a city use public transportation to get to work. A transit authority offers discount rates to companes that have at least 30 employees who use public transportation to get to work. You randomly select 3 companies and ask their employees if they use public transportation below. Complete parts (a) through (c).

(a) Company A has 284 employees. What is the probability that Company A will get the discount.

(b) Company B has 542 employees. What is the probability that Company B will get the discount.

(c) Company C HAS 1038 employees. What is the probability that Company C will get the discount.

Explanation / Answer

p = 0.05

P(X>= 30) = P(X > 29.5) continuity correction

E(X) = np

sd(X) = sqrt(np*(1-p))

a) here n = 284

hence

mean = 284*0.05 = 14.2

sd(X) = sqrt(284*0.05*0.95) = 3.672873

P(X> 29.5)

=P(Z> (29.5 -14.2 )/3.672873 )

= P(Z> 4.165676297)

=0.000016

b)n = 542

P(Z > (29.5 - (542*0.05))/sqrt(542*0.05*0.95))

=P(Z> 0.473)

= 0.3181

c) here n = 1038

P(X> 29.5)

= P(Z>   (29.5 - (1038 *0.05))/sqrt(1038 *0.05*0.95))

=P(Z> -3.19)

=0.9993

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.