Solve the following problems involving normal distributions and
standard deviation.
If the question presents a situation that can be solved using
increments of onehalf
of one standard deviation, use the chart (below). If not, use
your graphing calculator.
1. 
The amount of mustard dispensed from
a machine at The Hotdog Emporium is
normally
distributed with a mean of 0.9 ounce and a standard
deviation of 0.1 ounce. If the machine is used
500 times, approximately how many times will it be
expected to dispense 1 or more ounces of mustard.
Choose:

Answer 

2. 
Professor Halen has 184 students in his college
mathematics lecture class. The scores on the midterm exam are
normally distributed with a mean of 72.3 and a standard deviation of
8.9. How many students in the class can be expected to receive
a score between 82 and 90? Express answer to the nearest
student.

Answer 

3. 
A machine is used to
fill soda bottles. The amount of soda
dispensed into each bottle varies slightly.
Suppose the amount of soda dispensed into the
bottles is normally distributed. If at least
99% of the bottles must have between 585 and 595
milliliters of soda, find the greatest standard
deviation, to the nearest hundredth, that can
be allowed. 
Answer 

4. 
Residents
of upstate New York are accustomed to large amounts of
snow with snowfalls often exceeding 6 inches in one day.
In one city, such snowfalls were recorded for two
seasons and are as follows (in inches):
8.6, 9.5, 14.1, 11.5, 7.0, 8.4, 9.0, 6.7, 21.5, 7.7,
6.8, 6.1, 8.5, 14.4, 6.1, 8.0, 9.2, 7.1
What are the mean and the population standard deviation
for this data, to the nearest hundredth?

Answer 

5. 
Neesha's scores in Chemistry this semester were rather
inconsistent: 100, 85, 55, 95, 75, 100.
For this population, how many scores are within
one standard deviation of the mean?

Answer 

6. 
Battery
lifetime is normally distributed
for large samples.
The mean lifetime is 500 days and the standard deviation
is 61 days. To the nearest percent, what
percent of batteries have lifetimes longer than 561
days?

Answer 

7. 
The
number of children of each of the first 41 United
States presidents is given in the accompanying
table. For this population, determine the mean
and the standard deviation to the nearest tenth.
How many of these presidents fall
within one standard deviation of the mean?
Answer 


8. 
From
1984 to 1995, the winning scores for a golf tournament were 276, 279,
279, 277, 278, 278, 280, 282, 285, 272, 279, and 278. Using the
standard deviation for this sample, S_{x}, find the
percent of these winning scores that fall within one standard deviation
of the mean.

Answer 

9. 
A shoe
manufacturer collected data regarding men's shoe sizes and found that
the distribution of sizes exactly fits the normal curve. If the
mean shoe size is 11 and the standard deviation is 1.5, find:
a. the probability that a man's shoe size is greater than or equal
to 11.b. the probability that a man's shoe
size is greater than or equal to 12.5.
c.

Answer 

10. 
Five
hundred values are normally distributed
with a mean of 125 and a
standard deviation of 10.
a. What percent of the values lies in the interval 115  135,
to the nearest percent?
b. What percent of the values is in the interval 100  150,
to the nearest percent?
c. What interval about the mean includes 95% of the data?
d. What interval about the mean includes 50% of the data?

Answer 

11. 
A
group of 625 students has a mean age of 15.8 years with a standard
deviation of 0.6 years. The ages are
normally distributed. How many students are younger
than 16.2 years? Express answer to the nearest student? 
Answer 

