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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 $502 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 $477 and $527? (c) Calculate the likelihood that the sample mean is between $492 and $512. (d) What is the probability that the sample mean is greater than $550?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 distblgted 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 8.0 years. (b) Find the probability that a randomly selected CD player will have a replacement time of more than 9.0 years. (c) Find the probability that a randomly selected CD player will have a replacement time between 5 and 8 years. (d) Find the probability that a randomly selected CD player will have a replacement time of less than 5.1 or greater than 9.1 years. 2. (a) A news report stated that 65% of the vehicles sold nationally were SUVs. A random sample of 100 vehicles sold in the last month is taken. What is the probability that at least 70 of the vehicles in the sample were SUVS? (10 points) (b) A local orist says that 85% of all owers sold for Valentine's Day are roses. Consider a random sample of 150 orders for Valentine's Day owers. What is the probability that less than 80% of the orders in the sample are for roses? (10 points) Fill in the Blank. (2 points each) 1. The standard error of the mean equals the populati square root of the . between a sample mean and the population mean is called the on standard deviation divided by the 2. The difference _________._ 3. The mean of all possible sample means is than, always smaller than, always equal to, 4. If a population follows the normal distribution, what will be the shape of the distribution of sample means? the population mean. (always larger not a constant relationship with) is a single-number estimate of a population parameter. 6. The fraction or percentage of a sample that has a certain characteristic is called a _________________. what is true about the mean, and median? (always equal, the 7. For a normal distribution, the mean and median are equal to the standard deviation, none mean is twice the median, of these is true pick one) 8. What is the probability of a z-value between -1 .26 and 2.39? 9. A data set has a mean of 720 and a standard deviation of 6. Which is closest to the z-score of an element of this data set with a value of 709? (a) 11.00 (b) 1.83 (c) .1100 (d) -1.83 10. The mean distance a new sales representative travels per week in the rst year is 300 miles. At Olivia's job interview, she found out that she would travel at most the mean distance per week for rst-year sales reps. Which of the following z-scores are possible for her mean weekly traveling distance during her rst year? ' (a) 0 (b) -1.42 (c) 0.78 (d) Not enough information