Question

Overall, the amount of study-hours involved in preparing for the Programming Competition is normally distributed around 150 hours with a standard deviation of 20 hours.

a) What’s the probability that the mean number of study-hours will be between 160 and 165?

b) Students at or below the 15%ile of number of study-hours must attend a one-on-one meeting with their advisor. At least how many study-hours you should have in order to avoid attending such session?

c) How likely (what is the probability) is it to have the number of study-hours below 130?

d) How likely (what is the probability) is it that some students will have his/her study-hours between 120 and 140?

Answer 1

Let X denote the number of study hours involved in preparing for the Programming Competition. Then

a)

b)

Let 'a' denote the number of hours required to avoid the session. Then,

c)

Required probability =

d)

Required probability =