Five percent of workers in a city use public transportation to get to work. A tr
ID: 3246222 • Letter: F
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
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.