The times per week a student uses a lab computer are normall

The times per week a student uses a lab computer are normally distributed, with a mean of 6.1 hours and a standard deviation of 1.4 hours. A student is randomly selected. Find the following probabilities. (a) Find the probability that the student uses a lab computer less than 4 hours per week. (b) Find the probability that the student uses a lab computer between 6 and 8 hours per week. (c) Find the probability that the student uses a lab computer more than 9 hours per week.

Solution

mean : 6.1 hour

standard deviation: 1.4 hours

a) P<= 4 hours x week

x=4 z= (4-6.1)/(1.4) =-1.5 so the probability P=>-1.5 is = 0.0668

b) 6<= P=> 8 hour x week

x=6 z= (6-6.1)/(1.4) =-0.071 so the probability P=>-0.071 is = 0.4721

x=8 z= (8-6.1)/(1.4) = 1.36 so the probability P=>1.36 is =0.0869

so the probability (6<= P=> 8)=0.4721-0.0869 =0.3852, take into account the probability of positive Z to right wing and if the number is negative to the left

c) P>9 hour x week

x=9 z= (9-6.1)/(1.4) = 2.07 so the probability P=>2.07 is = 0.0192