Concept explainers
a.
Find the probability that no stolen goods are recovered in 170 or more of the robberies.
a.
Answer to Problem 7SR
The probability that no stolen goods are recovered in 170 or more of the robberies is 0.0465.
Explanation of Solution
It is given that none of the stolen goods are recovered by the homeowners in 80% of reported theft. The total number of theft occurred at certain period of time is 200 and corresponding distribution is binomial.
That is,
The mean can be obtained as follows:
The standard deviation can be obtained as follows:
The probability that no stolen goods are recovered in 170 or more of the robberies can be found as follows:
Step-by-step procedure to obtain the probability using Excel:
- Click on the Formulas tab in the top menu.
- Select Insert
function . Then from category box, select Statistical and below that NORM.S.DIST. - Click Ok.
- In the dialog box, Enter Z value as 1.68.
- Enter Cumulative as TRUE.
- Click Ok, the answer appears in the spreadsheet.
Output obtained using Excel is represented as follows:
From the above output, the probability of Z less than 1.68 is 0.9535.
Consider,
Thus, the probability that no stolen goods are recovered in 170 or more of the robberies is 0.0465.
b.
Find the probability that no stolen goods are recovered in 150 or more robberies.
b.
Answer to Problem 7SR
The probability that no stolen goods are recovered in 150 or more robberies is 0.9679.
Explanation of Solution
The probability that no stolen goods are recovered in 150 or more robberies can be obtained as follows:
Step-by-step procedure to obtain the probability using Excel:
- Click on the Formulas tab in the top menu.
- Select Insert function. Then from category box, select Statistical and below that NORM.S.DIST.
- Click Ok.
- In the dialog box, Enter Z value as –1.85.
- Enter Cumulative as TRUE.
- Click Ok, the answer appears in the spreadsheet.
Output obtained using Excel is represented as follows:
From the above output, the probability of Z less than –1.85 is 0.0321.
Now, consider
Therefore, the probability that no stolen goods are recovered in 150 or more robberies is 0.9679.
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Chapter 7 Solutions
Statistical Techniques in Business and Economics, 16th Edition
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