Please show all working Answer all quesiions Question 1 |5 marks| c) A local jam production company is confident that 60% of the population will like its new grapefruit jelly. (i) If 200 persons taste the new grapefruit jelly, determine the number of persons who are expected to like it. [2] (ii) From a random sample of 10 persons who tasted the new grapefruit jelly, calculate the probability that less than two will like it. [3] Question 2 |16 marks| In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company,r wants to perform a test to determine whether this average duration of long distance calls has changed. Fifty calls, originating from the town, was randomly selected and the following summary minutes. Ex = 205 Zia5:52 = 56.43 a) Calculate the sample mean, )5. [2] b) Calculate the sample standard deviation. [3] c) Using the p value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased. [8] d) Construct the 99% condence interval for the population mean duration of the long-distance calls from the town. [3]