Introduction to Business Statistics
Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
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Chapter 6, Problem 6.54CE

The owner of a charter fishing boat has found that 12% of his passengers become seasick during a half- day fishing trip. He has only two beds below deck to accommodate those who become ill. About to embark on a typical half-day trip, he has 6 passengers on board. What is the probability that there will be enough room below deck to accommodate those who become ill?

Expert Solution & Answer
Check Mark
To determine

To find:

The probability of having enough room to accommodate the ill

Answer to Problem 6.54CE

The probability of having enough room to accommodate the illis 0.02

Explanation of Solution

Given:

12% of passengers become seasickThere are only two beds to accommodate the ill

There are 6 passengers

Formula used:

The formula for a Binomial Distribution is

The probability of exactly x successes in n trials is

  P(x)=n!x!(nx)!πx(1π)nx

Where n= number of trials

x= the number of successes

  π = the probability of success in any given trial

  (1π) = the probability of failure in any given trial

Calculation:

In this problem, a binomial distribution is accurate to use because there are two or more consecutive trials (the six people on board the boat) and there are only two possible, independent outcomes(get sick or not). Using the equation above we can calculate the probability that P(X>2) when x= the number of people who get sick.

  P(X>2)=P(X=3)+P(X=4)+P(X=5)+P(X=6)

The calculation for P(X=3) is

   P(X=3)= 6! 3!(63)! (0.12) 3 (0.88) 63

                  =20× (0.12) 3 (0.88) 3 =0.02

The calculation for P(X=4) is shown below:

   P(X=4)=15× (0.12) 4 (0.88) 2 6! 4!(64)! (0.12) 4 (0.88) 64

                  =15× (0.12) 4 (0.88) 2 =0.002

Because P(X=4) = approximately zero we can assume that P(X=5) and P(X=6) will also be zero.

Adding up these probabilities we can determine the probability that P(X=2).

  0.02+0.00=0.02

Because this probability is so low, it is very unlikely that the owner of the boat will run out of beds below deck.

Conclusion:

Thus, the probability of having enough room to accommodate the illis 0.002

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Chapter 6 Solutions

Introduction to Business Statistics

Ch. 6.1 - A consultant has presented his client with three...Ch. 6.1 - Prob. 6.12ECh. 6.1 - Prob. 6.13ECh. 6.1 - Laura McCarthy, the owner of Riverside Bakery, has...Ch. 6.1 - In 2007, nearly 24 million tons of steel mill...Ch. 6.2 - What is necessary for a process to be considered a...Ch. 6.2 - When we are sampling without replacement, under...Ch. 6.2 - Prob. 6.18ECh. 6.2 - Prob. 6.19ECh. 6.2 - A city law-enforcement official has stated that...Ch. 6.2 - Prob. 6.21ECh. 6.2 - According to the National Marine Manufacturers...Ch. 6.2 - In the town of Hickoryville, an adult citizen has...Ch. 6.2 - It has been reported that the overall graduation...Ch. 6.2 - Prob. 6.25ECh. 6.2 - The U.S. Department of Labor has reported that 30%...Ch. 6.2 - Alicia’s schedule includes three Tuesday/Thursday...Ch. 6.2 - OfficeQuip is a small office supply firm that is...Ch. 6.2 - Four wheel bearings are to be replaced on a...Ch. 6.2 - It has been estimated that one in five Americans...Ch. 6.2 - Airlines book more seats than arc actually...Ch. 6.2 - Every day, artists at Arnold’s House of Fine...Ch. 6.3 - Under what circumstances should the hypergeometric...Ch. 6.3 - Using the hypergeometric distribution, with...Ch. 6.3 - Using the hypergeometric distribution, with...Ch. 6.3 - In a criminal trial, there are 25 persons who have...Ch. 6.3 - A computer firm must send a group of three...Ch. 6.3 - Prob. 6.38ECh. 6.4 - Prob. 6.39ECh. 6.4 - Prob. 6.40ECh. 6.4 - Prob. 6.41ECh. 6.4 - Prob. 6.42ECh. 6.4 - The U.S. divorce rate has been reported as 3.6...Ch. 6.4 - During the 12 P.M.-1 P.M. noon hour, arrivals at a...Ch. 6.4 - During the winter heating season in a northern...Ch. 6.4 - Prob. 6.46ECh. 6.4 - Prob. 6.47ECh. 6.4 - Prob. 6.48ECh. 6.4 - Prob. 6.49ECh. 6.4 - A manufacturing plant’s main production line...Ch. 6.4 - Prob. 6.51ECh. 6 - The owner of a charter fishing boat has found that...Ch. 6 - Prob. 6.55CECh. 6 - Prob. 6.56CECh. 6 - Prob. 6.57CECh. 6 - Prob. 6.58CECh. 6 - Prob. 6.59CECh. 6 - Prob. 6.60CECh. 6 - A mining company finds that daily lost-work...Ch. 6 - Prob. 6.62CECh. 6 - Prob. 6.63CECh. 6 - Prob. 6.64CECh. 6 - Prob. 6.65CECh. 6 - Seven of the 15 campus police officers available...Ch. 6 - Prob. 6.67CECh. 6 - Prob. 6.68CECh. 6 - Prob. 6.69CECh. 6 - Prob. 6.70CECh. 6 - Prob. 6.71CECh. 6 - Prob. 6.72CECh. 6 - Prob. 6.73CECh. 6 - Prob. 6.74CECh. 6 - Prob. 6.75CECh. 6 - Prob. 6.76CECh. 6 - Prob. 6.77CECh. 6 - Prob. 6.78CECh. 6 - Prob. 6.79CECh. 6 - Prob. 6.80CE
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