The Center of Disease Control and Prevention reported the diastolic blood pressure of adult women in the US are approximately normally distributed with a mean of 80.5 and standard deviation of 9.9 . An adult female has her blood pressure checked.
a) What is the probability her diastolic blood pressure is above 110?
b) What value represents the 33rd percentile?
c) A doctor places 37 adult women on the same diet plan. At their 4 week check-up, their average diastolic blood pressure is 75.6. What is the probability their average is not more than 75.6?
d) Should the doctor be concerned? Explain your answer.