6 IA124-3-FY Question 10 a) A birthday cake delivery company delivers cakes to customers in an average time of 48 hours after the order was placed, with a standard deviation of 3 hours. Assume that delivery times are normally distributed. What is the z-score for a cake that was delivered 52 hours after the order was placed? ii ) What percentage of cakes are delivered in less than 52 hours? b) A survey of 100 students found that the average time spent travelling to university last week was 6 hours with a standard deviation of 4 hours. Conduct a hypothesis test at the 5% significance level to examine whether the average time spent travelling to university for all students is exactly 5 hours or more than 5 hours. Note: In your solution, you should include the null and alternative hypotheses, the critical value, the test statistic value, and the decision made