1. Problem 7.1 Given a normal distribution with u= 100 and o=10, if you select a sample of n=25, what is the probability that the sample mean is a. less than 95? b. between 95 and 97.5? c. above 102.2? d. There is a 65% chance that sample mean is above what value? 2. Problem 7.5 The amount of water in a two-liter bottle is approximately normally distributed with a mean of 2.05 liters with a standard deviation of 0.025 liter. a. What is the probability that an individual bottle contains less than 2.03 liters? b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is less than 2.03 liters? c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is less than 2.03 liters? d. Explain the difference in the results in (a) and (c). e. Explain the difference in the results in (b) and (c). 3. Problem 7.9 According to a report by App Annie, a business intelligence company that produces tools reports for the apps and digital goods industry, smartphone owners are using an average of 30 apps per month. Assume that number of apps used per month by smartphone owner is normally distributed and that the standard deviation is 5. If you select a random sample of 25 smartphone owners, a. What is the probability that the sample mean is between 29 and 31? b. What is the probability that the sample mean is between 28 and 32? If you select a random sample of 100 smartphone owners, what is the probability that C. the sample mean is between 29 and 31? d. Explain the difference in the results of (a) and (c) 4. Problem 7.17 The goal of corporate sustainability is to manage the environmental, economic, and social effects of a corporation's operations so it is profitable over the long-term while acting in a responsible manner to society. An international study by Unilever reveals that 33% of consumers are choosing to buy from brands they believe are doing social or environmental good. Suppose you select a sample of 100 consumers. a. What is the probability that in the sample fewer than 30% are choosing to buy from brands they believe are doing social or environmental good? b. What is the probability that in the sample between 28% and 38% are choosing to buy from brands they believe are doing social or environmental good? c. What is the probability that in the sample more than 38% are choosing to buy from brands they believe are doing social or environmental good? 5. Problem 7.23 Why does the sampling distribution of the mean follow a normal distribution for a large enough sample size, even though the population may not be normally distributed