Calculating Time of Departure You have a 5:30 PM flight from the airport on Thur

Question

Calculating Time of Departure You have a 5:30 PM flight from the airport on Thursday and need to decide the time of departure from your home. The times in the table below are based on the average times and standard deviations for travel time, parking, check-in, and security for Thursday afternoon. Travel Time Parking Check-in Mean 55 minutes 18 minutes 38 minutes Standard Deviation 23 minutes 8 minutes 24 minutes 21 minutes Security32 minutes Assume the distribution for each line item in the table above is bell-shaped and symmetrical and that the total average time and total standard deviation is given below. Total average time Total of individual means Total standard deviation Total variance You would like to be 99.7% certain that you will arrive at the gate before 5:00 PM.

Explanation / Answer

1.) Standard Deviation = 40.12

Total Mean = 143

Since we want to find 99.7% Confidence interval,

Let' first find Standard Error of Mean(Sm) = standard deviation / (100-99.7) = 40.12 / 0.3 = 133.73

Since we know standard deviation, so we can use normal distribution.

Now, z-score for 99.7% confidence interval is 3.0

The formula for estimation is:

? = M ± Z(sM)

where:

M = sample mean
Z = Z statistic determined by confidence level
SM = standard error of mean

Since, we want to find how many hours before we should leave to reach Airport by 5:00 PM. So only lower limit is required which is given as:

? = 143 - 3 * 133.73

? = 143 - 3 * 133.73

? = -256 minutes = -4.2 hrs

Minus Sign shows that we have to leave atleast 4.2 hrs before to be 99.7% sure to reach Airport by 5:00 PM

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