Name________________________
Date _________
Introduction to Probability & Statistics
Ch.5 Review
1.
If light bulbs have lives that are normally distributed with a mean of 2500 hours and
a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the
percentage of light bulbs having a life between 2000 hours and 3500 hours?
2. The average height of women is 65 inches with a standard deviation of 3 inches.
What percentile does Jane fall in if she is 5’1”? And what does this suggest?
3. The mean annual mileage of cars for a rental car fleet is 12,000 miles with a standard
deviation of 2,415 miles. If 225 cars were sampled what is the chance that the mean
of the distribution of sample means is less than 10,000 miles?
4. The mean life of light bulbs is 2500 hours with a standard deviation of 500 hours. If
300 bulbs were tested individually, approximately how many would have a lifetime
between 2000 and 3000 hours?
5. Determine whether each statement is true or false.
a. A z-score of 1.75 is considered unusual.
b. The standard deviation of a sample gets bigger as the sample size increases.
c. The area under the normal curve is 100%
d. The weight of all males in the U.S. would be best described as normal
e. The area to the left of the mean is negative.
6. Assuming the weights for a sample of cats are normally distributed with a mean of 11
pounds and a standard deviation of 2 pounds, find the following quantities using the
68-95-99.7 Rule.
a. Percentage of cats weighing less than 9 pounds.
b. Percentage of cats weighing more than 15 pounds.
c. Percentage of cats weighing between 13 and 15 pounds.
d. Percentage of cats weighing between 7 and 13 pounds.
7. The amount of Jen’s monthly phone bill is normally distributed with a mean of $60
and a standard deviation of $12. Fill in the blanks.
95% of her phone bills are between $________ and $________.
8. The annual precipitation amounts in a certain mountain range are normally distributed
with a mean of 88 inches, and a standard deviation of 10 inches. What is the
likelihood that the mean annual precipitation during 25 randomly picked years will be
less than 90.8 inches?
9. Assume that women have heights that are normally distributed with a mean of 65
inches and a standard deviation of 3 inches. Find the height that corresponds to the
93rd percentile.
10. The mean score on the exit examination for an urban high school is 63 with a
standard deviation of 8. What is the mean of the distribution of sample means with
a sample size of 9?
11. The diameters of bolts produced by a certain machine are normally distributed with
a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample
of 1500 bolts tested, how many will have a diameter greater than 0.32 inches?
12. A math teacher gives two different tests to measure students’ aptitude for math.
Scores on the first test are normally distributed with a mean of 24 and a standard
deviation of 4.5. Scores on the second test are normally distributed with a mean of
70 and a standard deviation of 11.3. Assume that the two tests use different scales to
measure the same aptitude. If a student scores 29 on the first test, what would be his
equivalent score on the second test? (That is, find the score that would put him in the
same percentile.)
13. A bank’s loan officer rates applicants for credit. The ratings are normally distributed
with a mean of 200 and a standard deviation of 50. If an applicant is randomly
selected, find the probability of a rating that is between 190 and 230.
14. A rocket club makes its own rockets. The rockets go to a mean height of 1100 feet
with a standard deviation of 60 feet. If the club fires 100 rockets, what is probability
that the mean height of the rockets will be between 1020 and 1150 feet?