The time needed to complete a final examination in a particu

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.
(a) What is the probability of completing the exam in one hour or less (keep answer at 4 decimals)?

(b) What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (keep answer at 4 decimals)?

2. Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.

(a) What is the probability of generating a random number between 0.15 and 0.85 (to 1 decimals)?

(b) What is the probability of generating a random number with a value less than or equal to 0.4 (to 1 decimals)?

(c) What is the probability of generating a random number with a value greater than 0.7 (to 1 decimals)?

(c) Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the nearest whole number)?

Solution

a) P(z < 60) = P (z < (60-80)/10) = P (z <-2) = 0.0228 or 2.28%

b) P(60 < z < 75) = P ((60 - 80)/10 < z < (75-80)/10) = P (-2.00 < z < -0.50) = 0.3085 - 0.0228 = 0.2858 or 28.58%