Answer :
The sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento within 5 minutes with 95% confidence is approximately 223.
To determine the sample size necessary to estimate the mean arrival delay time for American Airlines flights from Dallas to Sacramento within a certain margin of error and confidence level, we can use the formula for sample size calculation:
n = (Z² * σ²) / E²
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (for 95% confidence level, Z ≈ 1.96)
σ = standard deviation of the population
E = desired margin of error
In this case, we want to estimate the mean arrival delay time within 5 minutes (E = 5 minutes) with 95% confidence (Z ≈ 1.96), and the standard deviation is given as σ = 38.1 minutes.
Plugging these values into the formula, we get:
[tex]n = (1.96^2 * 38.1^2) / 5^2[/tex]
Calculating this expression:
n = (3.8416 * 1456.61) / 25
n ≈ 222.48
Rounding up to the nearest whole number, the sample size necessary to estimate the mean arrival delay time is approximately 223.
Learn more about standard deviation here: https://brainly.com/question/29115611
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