Download 1/4 Normal Distribution HW

FST
68-95-99.7 Rule
Name_________________________
1. The distribution of heights of Clayton High students is approximately normal with a
mean of 172cm and a standard deviation of 7 cm.
a. Label the graph including the mean, ±1s , ±2s , ±3s .
b. What percent of these data are within two standard deviations of the mean? (Shade the
curve to indicate the region.)
c. What percent of these data are more than 1 standard deviation above the mean?
(Shade the curve to indicate the region.)
d. What percent of the students are less than 186 cm tall? (Shade the curve to indicate the
region.)
e. What percent of the students are between 165cm and 186 cm tall? (Shade the curve to
indicate the region.)
2. The scores on a FST test are normally distributed with a mean of 80 points and a
standard deviation of 5 points.
a.
Sketch a normal distribution curve of this situation.
b.
What percentage of students scored more than 70 points?
c.
What percentage of students scored between 70 and 85 points?
3. When a machine that shapes wire clothes hangers is working properly, the lengths of the
bottom of the hangers are normally distributed with mean 16.5 inches and standard
deviation 0.1 inches.
a. If the machine is working properly, what percent of hangers will be less than 16.5
inches across the bottom? More than 16.6 inches? Less than 16.35 inches? Explain or
show your work.
Less than 16.5 inches:
More than 16.6 inches:
Less than 16.35 inches:
b. If the hanger company wanted to be sure that at least 97.5% of the hangers were 16.5
or more inches long, where should the mean length be set and why? Assume the
distribution remains normal with standard deviation 0.1 inches.