Question

The BMI for female patients with Type II Diabetes is normally distributed with a mean of 35.96 and standard deviation 5.69. Use the Empirical Rule to answer part a.

1. We expect 68% of females with Type II Diabetes to have a BMI between and
2. What is the probability that a randomly chosen woman with Type II Diabetes has a BMI less than 42.125?
   • z =
   • probability =
3. What is the probability that a randomly chosen woman with Type II Diabetes has a BMI greater than 30.99?
   • z =
   • probability =

Note: Round z-scores to 2 decimal places. All probabilities should be given to 4 decimal places.

Answer 1

a) By empirical rule:

68% range:

Between (35.96 - 5.69) and (35.96 + 5.69)

Between 30.27 and 41.65

b) z score for 42.125 = (42.125 - 35.96)/5.69 = 1.08

Probability = P(X < 42.125) = P(z < 1.08) = 0.8599

c) z score for 30.99 = (30.99 - 35.96)/5.69 = -0.87

Probability = P(X > 30.99) = P(z > -0.87) = 0.8078