Solve and show work respectively.

Free Response Question: You must show your work to earn full credit. 1. Find each specified probability. a. P(z > -1.78) (2 points) b. P(z 1.73) (3 points) 2. The accounting department at Weston Materials Inc., a natural manufacturer of unattached garages, reports that it takes two construction workers a mean of 30 hours and a standard deviation of 3 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. (a) Determine the z values for 27 and 35 hours. (15 points) (b) What percent of the garages take between 27 hours and 35 hours to erect? (c) What percent of the garages take between 31 hours and 36 hours to erect? (d) What percent of the garages take 29.3 hours or greater to erect? (e) Of the garages, 10% take how many hours to erect? 22. The IRS reports that the mean refund for a particular group of taxpayers was $1,500. The distribution of tax refunds follows a normal distribution with a standard deviation of $750. (a) What percentage of the refunds are between $1,500 and $2,100? (15 points) (b) What percentage of the refunds are between $800 and $1,900? (c) What percentage of the refunds are between $1,700 and $2,200? (d) What percentage of the refunds are less than $1,350? (e) Ninety percent of the refunds are less than what amount?Fill in the space. 1. (1 points each) What percentage of the values in a normal distribution are greater than the mean but less than two standard deviations above the mean? You can completely describe a normal distribution by two numbers, the and the A normal curve is symmetric about the mean, which tells us that the value of the mean equals the value of the and equals the value of the What is the area-under the curve of a normal distribution between one and three standard deviations below the mean? What is the probability of a 2 value between ~2.81 and 1.14? What is the probability of a 2 value greater than -0.81? What is the probability of a 2 value less than -2.39 or greater than 1.26? Circle the best answer for each of the following: (1 points each) 8. Suppose that a Normal model described student scores in a history class. Johnson has a standardized score (z-score) of +2.5. This means that Johnson A. is 2.5 points above average for the class B. is 2.5 standard deviations above average for the class C. has a standard deviation of 2.5 D. has a score that is 2.5 times the average for the class E. None of the above Let X represent a random variable whose distribution is Normal with a mean of 100 and a standard deviation of 10. Which of the following is equivalent to P(X > 115)? A. P(X