Free Response You Must Show Your Work to Earn Full Credit (20 points) 1. According to a recent report, replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. (a) Find the probability that a randomly selected CD player will have a replacement time of less than 6.0 years. (b) Find the probability that a randomly selected CD player will have a replacement time of more than 11.0 years. (c) Find the probability that a randomly selected CD player will have a replacement time between 4 and 10 years. (d) Find the probability that a randomly selected CD player will have a replacement time of less than 4.1 or greater than 8.1 years. 2. (a) A news report stated that 55% of the vehicles sold nationally were SUVs. A random sample of 200 vehicles sold in the last month is taken. What is the probability that at least 165 of the vehicles in the sample were SUVs? (10 points) (b) A local florist says that 70% of all flowers sold for Valentine's Day are roses. Consider a random sample of 180 orders for Valentine's Day flowers. What is the probability that less than 85% of the orders in the sample are for roses? (10 points)3. Human resource consulting (HRC) surveyed a random sample of 60 Twin Cities construction companies to find the information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is $602 with a standard deviation of $100. (20 points) (a) Compute the standard error of the sample mean for HRC. (b) What is the chance HRC finds a sample mean between $577 and $627? (c) Calculate the likelihood that the sample mean is between $592 and $602. (d) What is the probability that the sample mean is greater than $650 but less than $400