norm_areas_key

1c answer pnorm ( 1.77 , lower.tail = TRUE ) ## [1] 0.9616364 pnorm ( 1.77 , lower.tail = FALSE ) ## [1] 0.03836357 1 – 0.9616 = 0.0384 1d -2.25 < z < 1.77 1d answer This is P( z < 1.77 ) - P( z < -2.25 ) We have these values from part (c) and part (a). 0.9616 – 0.0122 = 0.9494 pnorm ( 1.77 , mean = 0 , sd = 1 , lower.tail = TRUE ) - pnorm ( - 2.25 , mean = 0 , sd = 1 , lower.tail = TRUE ) ## [1] 0.949412 3

Step 1: Calculate the z scores for 40 and 55: x = 40 , z = 40 − 50 4 = − 2 . 0 x = 55 , z = 55 − 50 4 = 1 . 0 Step 2: For P(z < 1), choose Left-Tailed, input z-score of 1. OOMPH Stat returns auc: 0.8413 Step 3: For P(z < -2.00), choose Left-Tailed, input z-score of -2.00, OOMPH Stat returns auc: 0.0227 Step 4: The area we need is P( z < 1 ) - ( z < -2 ) Subtract 0.0227 from 0.8413 = 0.8186 6

5: Cholesterol in Middle-Aged Men exercise 11.36 in both 3rd and 4th editions The blood cholesterol levels of men aged 55 to 64 are approximately normal with mean 222 milligrams per deciliter (mg/dL) and standard deviation 37 mg/dL. 5a What percent of these men have high cholesterol (levels above 240 mg/dL)? 5a answer pnorm ( 240 , mean = 222 , sd = 37 , lower.tail = FALSE ) ## [1] 0.3133111 OOMPH Stat Step 1: Calculate the Z-score: (240 - 222) / 37 = 0.4865 Step 2: Choose Right-Tailed for the Type, Curve Attribute is z-score of .4865 Step 3: OOMPH Stat returns the Area Under the Curve of 0.3133 5b What percent of these men have elevated cholesterol (between 200 and 240 mg/dL)? 5b answer 9

6: Body Mass Index (BMI) in American Young Women adapted from Baldi and Moore exercise 11.39 in the 4th edition Your body mass index (BMI) is our weight in kilograms divided by the square of your height in meters. High BMI is a common but controversial indicator of overweight or obesity. A study by the National Center for Health Statistics found that the BMI values of American young women aged 20 to 29 follow a normal curve, approximately, with mean 26.8 kg m 2 and standard deviation 6.4 kg m 2 . 6a People with BMI less than 18.5 are considered underweight. According to this criterion, what percent of this population is underweight? 6a answer z score for 18.5 = 18 . 5 − 26 . 8 6 . 4 = − 1 . 297 pnorm ( - 1.297 , mean = 0 , sd = 1 , lower.tail = TRUE ) ## [1] 0.09731559 # or more directly: pnorm ( 18.5 , mean = 26.8 , sd = 6.4 , lower.tail = TRUE ) ## [1] 0.0973371 6b People with BMI ≥ 25 and less than 30 are considered overweight. According to this criterion, what percent of this population is overweight? 6b answer # P ( BMI < 30 ) - P( BMI < 25 ) pnorm ( 30 , mean = 26.8 , sd = 6.4 , lower.tail = TRUE ) - pnorm ( 25 , mean = 26.8 , sd = 6.4 , lower.tail = TRUE ) ## [1] 0.3022031 6c What percent of this population is obese, with a BMI ≥ 30? 6c answer 12