stats and probablity!

Question

e BMI for female patients with Type II Diabetes is normally distributed with a mean of 32.96 and standard deviation 6.75. 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 38.235?
3. z = 
4. probability = 
5. What is the probability that a randomly chosen woman with Type II Diabetes has a BMI greater than 15.01? 
6. z = 
7. probability = Hint: Don't forget that the table gives you areas to the left of the standardized value.

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

Answer 1

1. 68% of the normally distributed data will lie within 1 standard deviation of the mean, i.e., mean - 1 standard deviation, mean + 1 standard deviation. You are given the mean and standard deviation.
2. Z = (x - mean)/SD. Here x = 38.235. Mean and standard deviation is given

P(x < 38.235) = P(z < Z) - determine that from standard normal probability table or on calculator.

3.

Compute Z for x = 15.01

P(x > 15.01) = P(z> Z) = 1 - P(z < -Z) - determine that from standard normal probability table or on calculator