Over the long run, the average driving time to work is known to be normally distributed, with μ = 15.3 minutes, with σ = 2.2 minutes (i.e., these are population parameters). What is the probability that on any given day the drive time will be between 14 and 16 minutes?
First find upper and lower Z values using z = − / σ , then use the Standard Normal Table to find corresponding areas. You can try solving again using NORM.S.DIST function in EXCEL.
2. If we randomly select 20 drive times, what is the probability that the sample mean exceeds 16 minutes? Again, assume μ = 15.3 minutes and σ = 2.2 minutes. Use TWO different methods:
a. Find z = - over σ/n inside square root sign, then use NORM.S.DIST or the Standard Normal Table.
b. Find the answer directly using NORM.DIST. Be sure to use the standard error of the mean for the "standard_dev" entry in the Excel function.