times spent by students would be approximately normal with the mean = 40 minutes and the standard deviation = 6 minutes

Question

 

about how long should be allotted for exam if the professor want almost all ( say 97.5%) of the class to finish?

mean =40 SD = 6 

wants 97.5% to finish 

Answer 1

For a normal distribution with 97.5% confidence to finish,  look up in a normal table z = 1.96

this means 1.96*SD = 1.96*6 = 11.76 above the mean of 40 or 51.76 minutes