Question 3 [Past Year Question] (a) A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 15 minutes and half an hour. (i) What is the probability that the shopping time will be less than 25 minutes? (ii) What is the probability that the shopping time will be between 20 minutes and 50 minutes? (iii) Determine the mean time spent shopping in a supermarket for a market basket of 20 specific items. (b) Battery manufacturers compete on the basis of the amount of time their products last in scientific calculators. A manufacturer of such batteries has observed that the lifespan for their batteries is normally distributed with an average of 650 hours and a standard deviation of 1500 minutes. i) What is the probability that the battery lasts between 600 and 630 hours? ii) What is the probability that the battery lasts longer than 690 hours? iii) What is the minimum lifespan for 90% of the batteries? (c) In a poll conducted by the General Social Survey, 81% of respondents said that their jobs were sometimes or always stressful. Ten workers are chosen at random. i) Find the probability that at most 7 of them find their job stressful. ii) Find the probability that 5 or 6 of them find their job stressful. iii) Find the expected value and standard deviation for the number of respondents who does not find their job stressful.