A friend of mine just moved and now has to commute to work S

A friend of mine just moved and now has to commute to work. She wanted to figure out how long it would take her on most days, so she collected some data. Shefound that the average travel time was 43 minutes with a standard deviation of 2.5 minutes. Assuming her commute times are normally distributed, 95% of the timeshe should make it to the office between _____ and _____ minutes. (Choose the answers to correctly fill in the blanks.)

a. 40.85 and 45.15 minutes

b. 40.5 and 45.5 minutes

c. 38.0 and 48.0 minutes

d. 35.5 and 50.5 minutes

Solution

X is normal with mean = 43 and sigma = 2.5

If normal 95% of the time lie between -1.96 sigma and 1.96 sigma from mean

Or lower bound is 43-2.5(1.96) = (-38.3, 48.1)

Hence option c is very near to these

Option c

c. 38.0 and 48.0 minutes is the answer