Name ____________________________ Period _______
Precalculus – Math 3 review
Empirical Rule
1. Draw and label a normal distribution curve.
2. Given a group of data with a mean of 730 and a standard deviation of 40, what is the interval of data in
which 68% of the data would fall?
3. Find the mean and the standard deviation if 99.7% of a group of data lies between 75 and 93.
z-scores
4. For each pair of z-scores, find the area between them and the area outside of them.
a) 𝑧1 = −1, 𝑧2 = 1
b) 𝑧1 = 2, 𝑧2 = 2.5
c) 𝑧1 = −2.19, 𝑧2 = 2.19
5. For each area, find the number z so that the area between -z and z is the given area.
a) 0.50
b) 0.80
c) 0.97
6. A patient recently diagnosed with Alzheimer’s disease takes a cognitive abilities test. The patient scores a 45 on the
test (mean = 51, standard deviation of 4). What is this patient’s percentile rank?
7. Another patient with Parkinson’s disease takes the same cognitive abilities test as in the question above and scores a
57. What percent of individuals would receive a higher score?
The heights of 3000 women at a particular college are normally distributed with a mean of 65 inches and a standard
deviation of 2.5 inches.
8. What is the probability that a randomly selected college woman has a height of at most 68 inches,
𝑃(𝑥 ≤ 68)?
9. What is the probability that a randomly selected woman has a height of at least 64 inches, 𝑃(𝑥 ≥ 64)?
10. Using the sample, about how many college women have heights between 60 and 65 inches,
𝑃(60 ≤ 𝑥 ≤ 65)?
11. A test in economics has an average grade of 12 with a standard deviation of 3. The high score on the quiz was 20.
How many standard deviations above the mean did she score?
Binomial Distribution
The NOQC Company makes computer processing chips. Internal quality control has determined that 20% of all the
processing chips it manufactures are defective. PH Computers randomly samples its latest shipment of processing chips
from NOQC. If PH randomly samples 20 chips, what is the probability that:
12. Exactly 5 chips will be defective?
13. At most 3 chips will be defective?
14. Between 1 and 4 chips, inclusively, will be defective?