I'm unsure if I'm doing this problem correctly. Can I please get solutions with explanations

(20 points) Problem #8. For each trip to the grocery store, a shopper spends an average of 1=45 minutes with a standard deviation of o =12 minutes. The length of time spent in the store is normally distributed. (a) If one randomly chosen shopper is selected, what is the probability that his/her shopping time is within 5 minutes of the population mean? (b) Suppose random samples each consisting of 10 shoppers is selected and the mean time spent shopping is calculated for each sample of 10. What is the sampling distribution of the sample means? Justify your answer. BE SPECIFIC AND USE CLEAR, COMPLETE SENTENCES. (c) If ten shoppers are randomly selected, what is the probability that their mean time spent shopping is within 5 minutes of the population mean? (d) If twenty shoppers are randomly selected, what is the probability that their mean time spent shopping is within 5 minutes of the population mean