Concept explainers
(a)
Find the probability that the cycle time would exceed 60 minutes, given that it has exceeded 50 minutes.
(a)
Answer to Problem 40P
The probability that the cycle time would exceed 60 minutes, given that it has exceeded 50 minutes is 0.3132.
Explanation of Solution
Calculation:
Z score:
The number of standard deviations the original measurement x is from the value of mean
In the formula, x is the raw score,
The conditional probability formula is,
The variable x denotes the cycle time in minutes for the truck to leave the construction site.
The probability that the cycle time would exceed 60 minutes, given that it has exceeded 50 minutes is,
For
Substitute x as 60,
Use the Appendix II: Tables, Table 5: Areas of a Standard Normal Distribution: to obtain probability less than 1.25.
- Locate the value 1.2 in column z.
- Locate the value 0.05 in top row.
- The intersecting value of row and column is 0.8944.
The probability is,
For
Substitute x as 50,
Use the Appendix II: Tables, Table 5: Areas of a Standard Normal Distribution: to obtain probability less than 0.42.
- Locate the value 0.4 in column z.
- Locate the value 0.02 in top row.
- The intersecting value of row and column is 0.6628.
The probability is,
Substituting 0.1056 for
Hence, the probability that the cycle time would exceed 60 minutes, given that it has exceeded 50 minutes is 0.3132.
(b)
Find the probability that the cycle time would exceed 55 minutes, given that it has exceeded 40 minutes.
(b)
Answer to Problem 40P
The probability that the cycle time would exceed 55 minutes, given that it has exceeded 40 minutes is 0.3067.
Explanation of Solution
Calculation:
The probability that the cycle time would exceed 55 minutes, given that it has exceeded 40 minutes is,
For
Substitute x as 55,
Use the Appendix II: Tables, Table 5: Areas of a Standard
- Locate the value 0.8 in column z.
- Locate the value 0.03 in top row.
- The intersecting value of row and column is 0.7967.
The probability is,
For
Substitute x as 40,
Use the Appendix II: Tables, Table 5: Areas of a Standard Normal Distribution: to obtain probability less than –0.42.
- Locate the value –0.4 in column z.
- Locate the value 0.02 in top row.
- The intersecting value of row and column is 0.3372.
The probability is,
Substituting 0.2033 for
Hence, the probability that the cycle time would exceed 55 minutes, given that it has exceeded 40 minutes is 0.3067.
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