Download Word Processing

19
0
STAT101 Worksheet: Normal Distribution
1) Find the following:
P(2.4  z  1.27)
P(2.27  z  3.4)
2) IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Mensa is an organization
for people with high IQs, and eligibility requires an IQ above 131.5. If someone is randomly selected, find the
probability that he or she meets the Mensa requirement.
3) Using the information in the prior item, find the IQ score such that only 1% of the population exceeds it.
4) The U.S. Marine Corps requires that men have heights between 64 inches and 78 inches. Find the percentage of
men meeting those height requirements. (The National Health Survey shows that heights of men are normally
distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches)
5) Using the information given in the prior problem, what height corresponds to the 25 th percentile?
6) The speeds of cars traveling on Interstate 88 are normally distributed with a mean of 69 miles per hour and a
standard deviation of 3.5 miles per hour. Find what percentage of the cars traveling on this highway have a
speed of
a.) 61-66 miles per hour
b.) 66-74 miles per hour
c.) more than 74 miles per hour
7) The net amount of soda in a can of cherry cola has a normal distribution with a mean of 12 ounces and a
standard deviation of .015 ounces.
a) What is the probability that a randomly selected can of cherry cola contains 11.97 to 11.99 ounces of soda?
b) What percentage of soda cans contain more than 12.02 ounces of soda?
8) According to the U.S. Department of Agriculture, the mean yield of corn in 1998 was 84.6 bushels per acre.
Assuming that the 1998 yield of corn for all acres has a normal distribution with a mean of 84.6 bushels and a
standard deviation of 5.5 bushels, find the percentage of acres with 1998 yield of corn
a.)
b.)
c.)
d.)
less than 92 bushels
between 92 and 100 bushels
greater than 100 bushels
less than 69.2 bushels.