We will investigate the time spent in the mall, measured in minutes, of the shoppers in the dataset (variable time); call this variable X. Assume the population values of time are Normally distributed with mean 88 and standard deviation 5.
(a) Find the probability a shopper, selected at random, spends less than 96 minutes at the mall. Show your work. Write your final answer to 4 decimal places.
(b) Label the axis in terms of time, including the values for the individual in part (a) and the population mean. Shade the area representing the probability in part (a) and indicate its value.
(c) Label the axis in terms of z, including the values for the individual in part (a) and the population mean. Shade the area representing the probability in part (a) and indicate its value.
(d) What is the probability a shopper, selected at random, spends more than 98.5 minutes at the mall? Show your work. Round your final answer to 4 decimal places.
(e) What time value is the cut-off value for the top 15% of times? Show your work. You must start off by writing down the correct probability statement. (Round your final answer to 2 decimal places.)