(Show your calculation steps clearly. Correct you answer to 4 decimal places and report the measurement unit when applicable) Question 1 "FunBakery" is a bakery shop that customers can use the facilities to bake cakes. According to the record, the duration a customer spends in the shop follows a normal distribution with mean 140 minutes and standard deviation 18 minutes. (a) What is the probability that a customer stays in the shop for more than 3 hours? (b) There are 15% of all customers would stay in the shop for less than t minutes. Find the value of t. Round up the answer to the next integer. The charge in "FunBakery" is $100 for the first hour and then $1.1 per extra minute. (c) Find the average, median and standard deviation of the amount of money a customer spends in the shop. (d) For a customer stays in the shop for 3 hours, how much he / she needs to pay? (e) There are 15% of all customers would pay less than $k. Find the value of k by using your answer in part (b). (f) Write a simple summary about the spending of a customer in "FunBakery". Question 2 Jimmy is the education consultant of a tutorial school, which arranges preparatory classes for IELT examination. He randomly checks the mock examination result of 22 students in the school and the results are as follow: 7.9 8.2 7.8 5.4 6.8 6.8 7.1 7.2 7.9 8.1 7.6 7.8 5.8 6.3 7.7 7.7 8.3 8.3 4.7 5.1 7.3 6.5 (a) Write a report to reflect students' ability in the mock examination. The report needs to include the average performance, the median, the standard deviation, the bottom 20% and top 10% performance level. (b) The manager asks if the distribution of the examination result looks like a normal distribution. Answer his question by reviewing the skewness of the data with detailed calculation. (c) There are 18 students in Alex's class. By using the sampled data as a reference to project the chance an individual student can get more than 6 marks and assume students' result are independent, calculate the probability that more than 80% of Alex's students can score higher than 6 marks in the mock examination.