Question

. (a) Susan tries to exercise at ”Pure Fit” Gym each day of the week, except on the weekends (Saturdays and Sundays). Susan is able to exercise, on average, on 75% of the weekdays (Monday to Friday). i. Find the expected value and the standard deviation of the number of days she exercises in a given week. [2 marks] ii. Given that Susan exercises on Monday, find the probability that she will exercise at least 3 days in the rest of the week. [3 marks] iii. Find the probability that in a period of four weeks, Susan exercises 3 or less days in only two of the four weeks. [3 marks] (b) A car repair shop uses a particular spare part at an average rate of 6 per week. Find the probability that: i. at least 6 are used in a particular week. [2 marks] ii. exactly 18 are used in a 3-week period. [3 marks] iii. exactly 6 are used in each of 3 successive weeks. [3 marks] (c) The breaking strength (in pounds) of a certain new synthetic piece of glass is normally distributed, with a mean of 115 pounds and a variance of 4 pounds. i. What is the probability that a single randomly selected piece of glass will have breaking strength between 118 and 120 pounds? [2 marks] ii. A new synthetic piece of glass is considered defective if the breaking strength is less than 113.6 pounds. What is the probability that a single randomly selected piece of glass will be defective? [2 marks] iii. What is the probability that out of 200 pieces of randomly selected glass, more than fifty-five of them are defective. [5 marks]

Answer 1