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Honors Statistics
S6-2 Applications of the
Normal Distribution
NAME________________________
BLOCK_______________________
Questions 1 – 7, draw the normal distribution and label all appropriate areas on your
diagram.
1. What is the probability that a normally distributed random variable is not within 1.5
standard deviations of the mean?
2. Many students planning to go to college take the SAT examination. This test is
nationally normed with a mean of 540 and a standard deviation of 90. If Joe received a
625 mathematics score, what was his percentile score?
3. The mean and standard deviation of a normal distribution is 53 and 6 respectively.
Find the percentage of scores that are greater than 60.
4. A random variable x is normally distributed with a mean of 420 and a standard
deviation of 35. How many standard deviations is a score of 381 from the mean?
5. The sizes of the fish in a lake are normally distributed with a mean of 4.8 lbs. and a
standard deviation of 1.3 lbs. Through a catch and release program, park rangers
estimate that there are approximated 850 fish is the lake. Approximately how many fish
weigh between 5 and 5.4 lbs.?
6. A random variable x is normally distributed with an unknown mean and a standard
deviation of 7.24. If a score greater than 62 occurs approximately 85% of the time, find
the mean of this distribution to the nearest hundredth.
7a. Draw a normal curve that has a mean of 182 and a standard deviation of 18.
Label 3 standard deviations from the mean.
b. Using the distribution drawn in part a above, what is the probability that a score lies
between 174 and 186. Give your answer to 4 decimal places.
7b________
c. Using the distribution drawn in part a above, what is the probability that a score lies
between 166 and 176. Give your answer to 4 decimal places.
7c________
d. What is the minimum score to be in the top 8%.
7d________