You may find the probabilities using the Table or software of your choice. Please explain how you obtained your results.
The serum cholesterol levels in men aged 18-24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7. Units are mg/100 mL, and the data are based on the National Health Survey.
a. If one man aged 18-24 is randomly selected, find the probability that his serum cholesterol level is greater than 220.
b. If one man aged 18-24 is randomly selected, find the probability that his serum cholesterol level is between 165 and 200.
c. If 25 men aged 18-24 are randomly selected, find the probability that their mean serum cholesterol level is between 165 and 200.
d. The local hospital would wants to establish a criterion for recommending dietary changes if cholesterol levels are in the top 5%. What is the cutoff serum cholesterol for men aged 18-24?
The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculations, work, graphs and interpretations of the results are also included.