Density 0.04 Explain in plain language what is meant by "the sampling distribution of the sample mean.\" (2 marks) Suppose a population has mean ,u and standard deviation 0. What are the mean and standard deviation of all sample means, for samples of size n? (2 marks} Do your answers to question 5 depend on population shape? What about the sample size? (_;marks} There are two different conditions, under which the sampling distribution of the sample mean is approximately normal. What are these conditions? (2 marks) Let X denote the amount of time a randomly selected customer spends in a retail store. Suppose X follows a distribution with a mean of 10 minutes and a standard deviation of 6 minutes. Its density curve is given below. Population Distribution for Time Spent in Store 0.08 0.00 0 5 10 15 20 25 30 Time Spent in Store (min) a) Describe the shape of the population distribution(2 marks) b) If you randomly pick nine customers, describe the sampling distribution of the average time spent in the store; provide the mean, standard deviation, and shape. (3 marks) c) If you randomly pick 36 customers, describe the sampling distribution of the average time spent in the store; provide the mean, standard deviation, and shape. (3 marks) d) If you randomly pick 36 customers, find the probability that the average time spent in the retail store is at least 11.5 minutes. (4 marks)