Answer all the questions

Problem #1 The lifespan of domesticated cats is approximately normally distributed with mean of 15.9 years and standard deviation of 1.4 years a. What percent of domesticated cats live 18 years or longer? b. Find and interpret P2, the 20th percentile. Problem #2 A small bag of plain M&M's contains on average 56 candies. The number of candies in a bag is normally distributed with the standard deviation of 2.3 candies. Suppose a random sample of 10 small bags of plain M&M's is selected. What is the probability that in a random sample of 10 small bags of plain M&M's, the mean number of candies is 54 or fewer? Problem #3 A recent survey of a random sample of 100 American teenagers showed the average (mean) amount of time spent on recreational media was 8.5 hours per day with a standard deviation of 1.3 hours Find and interpret a 90 % confidence interval for the population mean. Problem #4 In 2015 American teens spent on average 7.3 hours on recreational media. A recent survey of a random sample of 100 American teenagers showed the average (mean) amount of time spent on recreational media was 8.5 hours per day with a standard deviation of 1.3 hours At a = .1 level of significance, test the claim that the mean time American teens spent on recreational media has increased since 2015 Problem 5 According to Pew Research Center survey, 67% of American teens say they use TikTok. Suppose a random sample of 5 American teens is selected. Let X be the number of teens in the sample who use TikTok a. Explain why X is a binomial random variable. Identify n (the number of trials), specify success and failure events (in words), and determine p (the probability of success). b. What is the probability that exactly 3 teens in the sample use TikTok? c. What is the probability that at least 2 teens in the sample use TikTok