"7 News" states that people either walk or cycle to school. The time taken to travel to school may be assumed to be independent and normally distributed. The mean and the standard deviation for these times are shown in the table below. Mean (minutes) Standard Deviation (minutes) Walking 30 Cycling 12 2 6 students are randomly selected, and their time taken to travel to school is recorded. Of the 6, 4 that were selected had walked to school, and 2 had cycled to school. a. Find the probability that the mean travelling time for the 6 students is less than 20 minutes. Give your answer correct to four decimal places. Someone called "10 News" complaining that the mean walking time to school is longer. To decide whether the mean time of walking to school is true, "10 News" selected a random sample of 50 students and found out that the mean time of this sample is 31 minutes. Let W denote the mean time (in minutes) of a random sample of 50 students walking to school. Testing at a significance 1% level of significance. b. State the null and alternative hypotheses c. Use the z-test to determine whether the complaint is valid, testing at a significance 1% level of significance. d. Find the maximum sample mean that could observe the null hypothesis to not be rejected. Give your answer correct to two decimal places. A proper review was conducted, revealing that the true mean time for walking to school is in fact 31 minutes. e. i. Find the probability that the null hypothesis will be accepted at a 1% level of significance. Give your answer correct to two decimal places. ii. Find the critical time that the probability that the null hypothesis will be accepted given the true mean time for walking to school is in fact 31 minutes, is equal to the probability that the null hypothesis will be rejected give the mean walking time is 30 minutes. Give your answer correct to two decimal places. iii. Find the probability that "10 News" can make the conclusion correctly. Give your answer correct to two decimal places