Question

You've surveyed the student body about time spent on coursework each week. The mean (??) is 8.3 hours with a standard deviation (??) of .85 hours. What is the probability of a student reporting working 10 hours or more each week on course work? What is the probability of a student reporting 5 hours or less on coursework? What proportion of students report doing coursework between 7 and 9 hours per week? How many hours would a student do coursework if he or she worked longer than 95% of other students?

Answer 1

We are given here for the time spent on coursework each week as:

Mean = 8.3 hours.
Std Dev. = 0.85 hours

a) The probability of working for 10 or more hours is computed here as:
P(X >= 10)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0228 is the required probability here.

b) The probability that the time is 5 hours or less is computed here as:

P( X< 5)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

therefore 0.0001 is the required probability here.

c) The proportion here is computed as:
P( 7 < X < 9)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here :

Therefore 0.7319 is the required probability here.

d) From standard normal tables, we have here:
P(Z < 1.645) = 0.95

Therefore the time here is computed as:
= Mean + 1.645* STd Dev

= 8.3 + 1.645*0.85

= 9.6983

Therefore 9.6983 hours is the required time here.