You plan to take a random sample of 36 students at your school to estimate the mean amount of time per week that students spend text messaging. The distribution of text time is not normal (for example a certain percentage of students never text). Unknown to you, the mean weekly text time for the population of students is 100 minutes, with a standard deviation of 60 minutes.

a) What is the shape of the sampling distribution for the sample mean text time for the 36 students in your sample? How do you know this? (3 marks)

b) Identify the mean and standard deviation of this sampling distribution. (4 marks)

c) Find the probability that your sample mean is not a very good estimate of the popula-tion mean, falling more than 20 minutes above or 20 minutes below the population mean. (4 marks)