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Course: STA416 - Applied Probability and Statistics

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QUESTION 4 a) The time it takes for a group of students to complete a Computer quiz is normally distributed with a mean of1 hour and a standard deviation of 12 minutes. i] It a student is selected at random, what is the probability that the time to complete the quiz is at least 75 minutes? (3 marks} ii} Find the probability that the time to complete the quiz is between 51'.) minutes to Tl] minutes. (3 marks} iii} It 65% of the students spend more than I minutes to complete the quiz, determine the value of t. (4 marks} b) A random variable '1' denotes the time {in hours) it takes to complete a programming course provided by JJ Centre. The probability density function of a random variable Y is given by: 3 2 {=07}: ELY 1). 153'53 I], elsewhere i] Calculate the probability that it takes more than 1.5 hours to complete the course. (3 marks} ii} Find the expected number of hours it takes to complete the course. (3 marks}