Final Answer:
We are 90% confident that the average airborne time for flights from San Francisco to Washington Dulles is between 241.7 and 258.3 minutes.
Step-by-step explanation:
A confidence interval is a range of values that is likely to contain the true population mean. The level of confidence indicates the probability that the true mean lies within the interval. In this case, we are 90% confident that the true mean airborne time for flights from San Francisco to Washington Dulles is between 241.7 and 258.3 minutes. This means that if we were to take many repeated samples of airborne times for flights from San Francisco to Washington Dulles, and construct a 90% confidence interval for each sample, 90% of the intervals would contain the true mean airborne time.
The confidence interval is calculated using the following formula:
mean ± (margin of error)
The margin of error is calculated using the following formula:
(z * standard deviation) / sqrt(sample size)
In this case, the mean airborne time is 249.5 minutes, the standard deviation is 5.2 minutes, and the sample size is 100. Plugging these values into the formula, we get:
249.5 ± (1.645 * 5.2) / sqrt(100)
249.5 ± 0.85
241.7 to 258.3
Therefore, we are 90% confident that the average airborne time for flights from San Francisco to Washington Dulles is between 241.7 and 258.3 minutes.