Download 1/4 Normal Distribution Notes

FST
Name_________________________
1. The normal distribution shown here has mean μ of 125 and standard deviation σ of 8.
a. On all three distributions, mark points along the horizontal axis that correspond to the
mean, one standard deviation above and below the mean, two standard deviations above
and below the mean, and three standard deviations above and below the mean.
b. On the first distribution, shade and label the region under the curve that represents 68%
of the data values.
c. On the second distribution, shade and label the region that represents 95% of the data
values.
d. On the third distribution, shade and label the region that corresponds to 99.7% of the
data values.
2. Suppose that the distribution of the weights of newly minted nickels is a normal distribution
with mean μ of 5 grams and standard deviation σ of 0.10 gram.
a. On the normal distribution, label the points on the horizontal axis that correspond to the
mean, one standard deviation above and below the mean, two standard deviations
above and below the mean, and three standard deviations above and below the mean.
b. What can you conclude about the middle 68% of the weights of these newly minted
nickels?
c. What can you conclude about the middle 95% of the weights?
d. What can you conclude about the middle 99.7% of the weights?
3. Consider the overall shape of a normal distribution.
a. What percentage of the values in a normal distribution lie above the mean?
b. What percentage of the values in a normal distribution lie more than two standard
deviations away from the mean?
c. What percentage of the values in a normal distribution lie more than two standard
deviations above the mean?
d. What percentage of the values in a normal distribution lie more than one standard
deviation away from the mean?
4. The weights of babies of a given age and gender are approximately normally distributed.
The table below gives information about the weights of six-month-old and twelve-monthold baby boys.
Weight at Six Months
(in pounds)
Mean
Standard
Deviation
Weight at Twelve Months
(in pounds)
17.25
22.50
2.0
2.2
a. On separate sets of axes, draw sketches that represent the distribution of weights for
six-month-old boys and the distribution of weights for twelve-month-old boys. How
do the distributions differ?
b. About what percentage of twelve-month-old boys weigh more than 26.9 pounds?
c. About what percentage of six-month-old boys weigh between 15.25 pounds and
19.25 pounds?
d. A twelve-month-old boy who weighs 24.7 pounds is at what percentile for weight?
e. A six-month-old boy who weighs 21.25 pounds is at what percentile?
5. Scores on the verbal section of the SAT I are approximately normally distributed with mean
μ of 500 and standard deviation σ of 100.
a. Draw a sketch to represent the distribution of scores.
b. What percentage of students score between 400 and 600 on the verbal section of the
SAT I?
c. What percentage of students score over 600 on the verbal section of the SAT I?
d. What percentage of students score less than 600 on the verbal section of the
SAT I?