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?