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Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 66e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 66e

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# An airport limousine can accommodate up to four passengers ISBN: 9780321629111 32

## Solution for problem 66E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 66E

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 20% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. a. ?If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip? b. ?If six reservations are made, what is the expected number of available places when the limousine departs? c. ?Suppose the probability distribution of the number of reservations made is given in the accompanying table. Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.

Step-by-Step Solution:

Answer : Step 1 of 3 : Given, An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 20% of all those making reservations do not appear for the trip a) If six reservations are made, the claim is to find the probability that at least one individual with a reservation cannot be accommodated on the trip Where, p = 0.80 and n = 6 P(at least one individual with a reservation cannot be accommodated on the trip) = P(x 5) = P(x = 5) + P(x = 6) 6 5 65 6 6 66 = ( 5(0.80) (1 0.80) + ( 6(0.80) (1 0.80) = (6) (0.32768) (0.20) + (1) (0.2621) ( 1) = 0.3932 + 0.2621 = 0.6553

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Step 3 of 3

##### ISBN: 9780321629111

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