Concept explainers
(a)
Find the probability that total taxi and take off time would be less than 320 minutes for 36 jets on a given runway.
(a)
Answer to Problem 22P
The probability that total taxi and take off time would be less than 320 minutes for 36 jets on a given runway is 0.8238.
Explanation of Solution
Calculation:
Central limit theorem:
The characteristics of the sampling distribution
Sampling distribution:
For x distribution the sampling distribution of
In the formula,
The
In the formula,
The random variable x is defined as taxi and take-off time for commercial jets. The
Consider the expression
The sum of taxi and take off time for 36 commercial jets on runway is denoted by w. That is,
The total taxi and take off time for 36 commercial jets on runway (w) is less than 320 can be written as,
Hence, the quantities
The number of commercial jets on runway in the study is
The mean of the x distributions is
The standard deviation of the x distributions is
Z score:
Substitute
Use the Appendix II: Tables, Table 5: Areas of a Standard Normal Distribution: to obtain probability less than 0.93.
- Locate the value 0.9 in column z.
- Locate the value 0.03 in top row.
- The intersecting value of row and column is 0.8238.
The probability is,
Hence, the probability that total taxi and take off time would be less than 320 minutes for 36 jets on a given runway is 0.8238.
(b)
Find the probability that total taxi and take off time would be more than 275 minutes for 36 jets on a given runway.
(b)
Answer to Problem 22P
The probability that total taxi and take off time would be more than 275 minutes for 36 jets on a given runway is 0.9808.
Explanation of Solution
Calculation:
The total taxi and take-off time for 36 commercial jets on runway (w) is more than 275 minutes has to be calculated which is denoted as
Consider the expression
The sum of taxi and take off time for 36 commercial jets on runway is denoted by w. That is,
The total taxi and take off time for 36 commercial jets on runway (w) is more than 275 can be written as,
Hence, the quantities
Z score:
Substitute
Use the Appendix II: Tables, Table 5: Areas of a Standard Normal Distribution: to obtain probability less than –2.07.
- Locate the value –2.0 in column z.
- Locate the value 0.07 in top row.
- The intersecting value of row and column is 0.0192.
The probability is,
Hence, the probability that total taxi and take off time would be more than 275 minutes for 36 jets on a given runway is 0.9808.
(c)
Find the probability that total taxi and take off time would be between 275 minutes and 320 minutes for 36 jets on a given runway.
(c)
Answer to Problem 22P
The probability that total taxi and take off time would be between 275 minutes and 320 minutes for 36 jets on a given runway is 0.8046.
Explanation of Solution
Calculation:
From part (a), the quantity 320 minutes is equal to 8.889 after conversion. The z score is 0.93. The probability value for less than 0.93 from normal table is 0.8238.
From part (b), the quantity 275 minutes is equal to 7.639 after conversion. The z score is
The probability is,
Hence, the probability that total taxi and take off time would be between 275 minutes and 320 minutes for 36 jets on a given runway is 0.8046.
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Chapter 6 Solutions
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