Statistics B
Chapter 6 Practice Test* ANSWERS
For #1 – 5, assume that Z has a standard normal distribution.
1. Find the probability that Z lies between –0.73 and +2.27. 0.7557 (calc: same)
2. Find the probability that Z is below +0.13.
0.5517 (calc: same)
3. Find the value of Z that separates the top 6% of values. 1.555 (between 1.55 and 1.56 inc
table) (calc: 1.55 – you wouldn’t know to use 3rd decimal place)
4. Find the value of “a” such that P(–a < Z < a) = 0.7814. 1.23† (calc: same)
†If
you answer “–1.23, that is fine, but the actual value of “a” is 1.23
5. Find the probability that Z is greater than +1.59.
0.0559 (calc: same)
6. If X is N(15.2, 0.9), find the probability that X is between 13.99 and 15.97. 0.7150 (calc:
0.7145)
7. If X is N(15.2, 0.9), find the probability that X is greater than 16.17.
0.1406)
0.1401 (calc:
8. If X is N(15.2, 0.9), find the values of X that contain the middle 25%.
(calc: 14.9 & 15.5)
14.912 & 15.488
9. Suppose that human body temperatures are N(98.20, 0.62). Find P5.
97.18 (calc: same)
10. If X is N(73, 7.8), find the probability that a sample of 24 values has a mean of more than 78.
0.0008 (calc: same)
11. If X is N(137,5.3), find the probability that X is less than 134.4.
0.3121 (calc: 0.3119)
12. If X is N(178.1, 40.7), find the values of X that separate the top and bottom 8%.
235.5 (calc: 120.9 & 235.3)
120.7 &
13. The diameters of pencils produced on a certain machine are normal distributed with a mean
of 0.30 inches and a standard deviation of 0.01 inches.
a. Find P80. Leave all four decimal places in your answer.
.3084 in (calc: same)
b. What is the probability that the diameter of a randomly selected pencil is less than 0.295
inches?
0.3085 (calc: same)
c. What is the probability that a sample of 20 pencils will have a mean diameter of less than
0.295 inches?
0.0125 (calc: 0.0127)
14. Explain whether or not the Central Limit Theorem can be used in each situation below.
a. Normally distributed population, sample size of n = 50.
YES – normal population
AND sample size of n > 30
b. Skewed population, sample size of n = 40.
size large enough)
YES – sample size of n > 30 (sample
c. Skewed population, sample size of n = 25.
size of n ≤ 30 (sample too small)
NO – skewed population and sample
d. Normally distributed population, sample size of n = 20.
(so sample size does not matter)
YES – normal population
15. In one region, the energy consumption levels for a particular month are N(1050, 218),
measured in kilowatt-hours (kWh).
a. Find the probability that the energy consumption of a randomly selected home is between
900 and 1200 kWh.
0.5098 (calc: 0.5086)
b. Find the two energy consumption levels that contain the middle 75% of values. 799.3 &
1300.7 (calc: 799.2 & 1300.8)
16. Assume that coin weights are N(5.67, 0.070), measured in grams.
a. What is the probability that a randomly selected coin will weigh more than 5.70 grams?
0.3336 (calc: 0.3341)
b. What is the probability that a roll of 40 coins will have a mean weight more than 5.70
grams?
0.0034 (calc: same)
c. Explain why the probability for the sample is so different than the probability for an
individual coin?
A sample should stick much closer to the mean than an
individual value, so for 40 coins to be, on average, above the mean is very unlikely.
17. A school gives a test to measure students’ aptitude. Scores are known to be normally
distributed with a mean of 68.0 and a standard deviation of 10.4. Find the sample size
needed to ensure with at least 99% probability, that the mean score will exceed 65? 65
18. The data below shows the number of texts sent in one class period by 40 randomly selected
high school students. Determine if the data come from a population that is normally
distributed. Explain your reasoning clearly. [On the test, you will be required to show me your
normal quantile plot on your calculator]
This data appears to come from a
normal distribution. A histogram
looks reasonably bell-shaped (bar
width of 5), and the normal quantile
plot follows a decent enough
straight-line patters
*because I wanted to keep this to one single page, the formatting is different from the actual
test…less space to show work, no answer blanks…