The mailing list of an agency that markets scuba-diving trips to the Florida Key
ID: 3253501 • Letter: T
Question
The mailing list of an agency that markets scuba-diving trips to the Florida Keys contains 55% males and 45% females. The agency calls 26 people chosen at random from its list. (a) What is the probability that 17 of the 26 people are men? (Use the binomial probability formula Round your answer to four decimal places.) (b) What is the probability that the first woman is reached on the 6th call? (That is, the first 6 calls give MMMMMF. Round your answer to four decimal places.) Although cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 66% of vehicles on the roads are occupied by just the driver. (Round your answers to four decimal places.) (a) If you choose 10 vehicles at random, what is the probability that more than half (that is, 6 or more) carry just one person? (b) If you choose 112 vehicles at random, what is the probability that more than half (that is, 57 or more) carry just one person? (Use the normal approximation.)Explanation / Answer
Answer:
9a)
n=26, p=0.55
P(X=x) = (nCx) px (1-p)n-x
P( x=17) = 0.0912
9b).
P =0.55*0.55*0.55*0.55*.055*0.45
=0.002265
=0.0023
10a).
n=10, p=0.66
P( x 6) =0.7730
b).
Expectation = np = 73.92
Variance = np(1 - p) = 25.1328
Standard deviation = 5.0133
Z value for 57 with continuity correction, z = (56.5-73.92)/5.0133 =-3.47
P( x57) = P( z >-3.47)
= 0.9997
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.