Suppose that the serum cholesterol levels of 17yearolds foll

Suppose that the serum cholesterol levels of 17-year-olds follow a normal distribution with a mean of 154 mg/dLi and a standard deviation of 30.0 mg/dLi. For each of the problems below, find the appropriate probability.
Note: For problems A, B, C, and D round your answers to four decimal places.

A) P(L 118.30)   

B) P(L > 142.00)   

C) P(103.90 L < 197.20)   

D) Serum cholesterol levels of 200 mg/dLi (or less) are considered good. What proportion of 17-year-olds have good cholesterol?  

E) The government is offering a free program to help 17-year-olds lower their cholesterol. Those in the 98^th percentile of all 17-year-olds are eligible for the program. What is the minimum cholesterol level one would need to qualify for the program?  

F) The serum cholesterol levels that enclose the central 95% of the distribution are:
    Note: Round your answers to two decimal places for this problem.
    Low: ______ to High: _______

Solution

a)

P(L<118.30)

= P(Z < 118.3 - 154/30)

= P(Z < -1.19)

= 0.1170

b)

P(L > 142) = P(Z > 142-154/30)

= P(Z > -0.4)

= 0.6554

c)

P(103.90 < L < 197.2)

= P(Z < 197.2 - 154 /30) - P(Z < 103.9 -154 /30)

= P(Z < 1.44) - P(Z < -1.67)

= 0.9251 - 0.0475

= 0.8776

d)

P(L < 200)

= P (Z < 200 -154/30)

= P(Z < 1.53333)

= 0.9374