Need help with the following questions
1. Applications of the Normal Distribution A sport psychologist has devised a stress test for hairline fracture patients sitting in the waiting rooms. According to this test, the stress scores (on a scale of 1 to 10) for patients waiting for hairline fracture are found to be approximately normally distributed with a mean of 7.59 and a standard deviation of .73. a. What percentage of such patients have a stress score lower than 6.0? b. What is the probability that a randomly selected hairline fracture patient sitting in the waiting room has a stress score between 7.0 and 8.0? c. The psychologist suggests that any patient with a stress score of 9.0 or higher should be given a sedative prior to treatment. What percentage of patients waiting for hairline fracture treatments would need a sedative if this suggestion is accepted? 2. Determining the z and x Values When an Area Under the Normal Distribution Curve Is Known According to the records of an electric company serving the Boston area, the mean electricity consumption during winter for all households is 1650 kilowatt-hours per month. Assume that the monthly electric consumptions during winter by all households in this area have a normal distribution with a mean of 1650 kilowatthours and a standard deviation of 320 kilowatt-hours. The company sent a notice to Bill Johnson informing him that about 90% of the households use less electricity per month than he does. What is Bill Johnson's monthly electricity consumption? 3. The Normal Approximation to the Binomial Distribution Stress on the job is a major concern of a large number of people who go into managerial positions. It is estimated that 80% of the managers of all companies suffer from jobrelated stress. a. What is the probability that in a sample of 200 managers of companies, exactly 150 suffer from job- related stress? b. Find the probability that in a sample of 200 managers of companies, at least 170 suffer from job related stress. c. What is the probability that in a sample of 200 managers of companies, 165 or fewer suffer from jobrelated stress? 4. Simple Linear Regression Analysis The recommended air pressure in a basketball is between 7 and 9 pounds per square inch (psi). When dropped from a height of5 feet, a properly inflated basketball should bounce upward between 52 and 56 inches. The basketball coach at a local high school purchased 10 new basketballs for the upcoming season, inflated the balls to pressures between 7 and 9 psi, and performed the bounce test mentioned above. The data obtained are given in the following table. -m- Bounoe height 54.1 54.3 55.2 53.3 55.4 52.2 55.7 54.6 54.8 55.3 (inches) a) With the pressure as an independent variable and bounce height as a dependent variable, compute Sxx, SSW, and SSxy. b) Find the least squares regression line. c) Interpret the meaning of the values of the a and b calculated in part b. d) Calculate r and r2 and explain what they mean. e) Compute the standard deviation of errors. f) Predict the bounce height of a basketball for x = 8.0
