The
cholesterol levels for healthy adults follow an approximate normal distribution
with mean 185 mg/dL and standard deviation 10 mg/dL. Notation for the distribution: N(185, 10). Using only the empirical rule (i.e., the 68-95-99.7 rule), answer the
following questions.
a. What percent of healthy
adults have cholesterol levels between 165 and 195 mg/dL?
b. What percent of healthy
adults have cholesterol levels above 215 mg/dL?
c. What percent of healthy
adults have cholesterol levels between 195 and 205 mg/dL?
Consider
the standard normal distribution, N(0, 1).
a. What is the area under
the curve to the left of 1.35?
b. What is the area under
the curve to the right of 1.35?
c. What is the area under
the curve between –1.21 and 0.80?
Example
3
The
exam scores for a statistics class follow an approximate normal distribution
with mean 68.2 points and standard deviation 12.5 points, N(68.2, 12.5).
a. What percent of the
scores are between 60 and 70 points?
b. Only students with
scores in the top 10% of the distribution receive an A. What is the
minimum score a student must get in order to receive an A?
Agricultural
scientists are working to develop an improved variety of Roma tomatoes.
Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of
Roma plants produces fruit that average 74 grams, but 11% of the tomatoes are
too small (i.e., weigh less than 70
grams). The weights of these tomatoes follow an approximate normal
distribution.
a. What is the standard
deviation of the weights of Romas now being grown?
b. Scientists hope to
reduce the frequency of undersized tomatoes to no more than 4%. One way to
accomplish this is to raise the average size of the fruit. If the standard
deviation remains the same, what target mean should they have as a goal?