STAT LAB ASSIGNMENT 4 Normal Distribution & Correlation and Regression 1. The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. a) What percent of people earn less than $40,000? b) What percent of people earn between $45,000 and $65,000? c) What percent of people earn more than $70,000? 2. A mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. a) The top 3% of students receive $500. What is the minimum score you would need to receive this award? b) The bottom 1.5% of students must go to summer school. What is the minimum score you would need to stay out of this group? 3. Find the area under the standard normal distribution curve of following: a. Between z = 0 and z= -0.32 b. To the right of z = 0.29 c. Find the z value for a cumulative probability of 0.5478 4. The following table gives information on weights (kg) and systolic blood pressure (m Hg) for a random sample of 10 adults. Weight (x): 67 69 85 74 81 97 92 114 85 SBP (y): 120 125 140 160 130 180 150 140 200 130 a. Make a scatter plot for these data and describe the relationship between weight and blood pressure. b. Find the correlation coefficient (r) between Weight and Blood Pressure. c. Determine whether there is a significant linear correlation between the two variables. d. If there is a positiveegative linear correlation, find the equation of the regression line. e. What is the best predicted blood pressure of a person whose weight is 65 kg? 83