Name: _____________________________________________________ Date: __________________________________ Period: ______
CHS Statistics
Section 5 Review
1. What do z-scores describe?
2. The mean sale per customer for 40 customers at a gas station is $36.00, with a standard deviation of
$8.
a. Draw The Normal Model that represents these data. Clearly label the model.
b. What percent of people purchase between $20 and $52 of gas? Assume that the data follow a
Normal distribution.
c. Between what two values to 99.7% of the sales lie?
d. What sale values represent the top 2.5%?
3. A certain brand of automobile tires has a mean life span of 35,000 miles. One tire’s actual lifespan
was 29,375 miles, which corresponds to a z-score of -2.5. Find the standard deviation of the lifespan
of this brand of tires.
4. Adult males have heights with a mean of 69.0 in and a standard deviation of 2.8 in. Former NBA
basketball player Shaquille O’Neal is 7’ 1” tall, and Bob Jenkins is 5’ 4” tall. Who is farther from the
mean in terms of standard deviations?
5. The Wechsler Adult Intelligence Scale (WAIS) is a common IQ test for adults. The distribution of
WAIS scores for persons 16 years or age of older is approximately normally distributed with mean
100 and standard deviation 15.
a. What is the probability that a randomly chosen adult has a WAIS score of 119 or more?
b. Suppose that a random sample of 25 adults is chosen. What is the probability that the average
of that sample will exceed 109?
6. A clothing manufacturer finds it unprofitable to make clothes for very tall or very short adult males.
American Eagle decides to discontinue production for the tallest 7½% and the shortest 7½% of
males. Find the minimum and maximum male heights for which American Eagle will have clothes.
Recall that µ = 69.0 inches and σ = 2.8 inches for males.
7. The diameters of bolts produced by a machine are normally distributed with a mean of 0.30 inches
and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than
0.32 inches?
8. For women 18-24, blood pressures are normally distributed with a mean of 114.8 mmHg and a
standard deviation of 13.1 mmHg. Doctors will treat patients with medication whose blood pressure
is too low or too high. Too low is defined as being in the bottom 10% of all blood pressures. What is
the maximum value for blood pressure for which a woman would be considered to be in the too low
group?
9. A study of the amount of time it takes a mechanic to rebuild the transmission for a Chevrolet Cobalt
shows the mean is 8.4 hours and a standard deviation of 1.8 hours.
a. If one mechanic is randomly selected, what is the probability that he rebuilds the transmission
between 8 and 9 hours?
b. If 40 mechanics are randomly selected, what is the probability that their mean rebuild time is
between 8 and 9 hours?
10. Suppose that IQs in the general population are normally distributed with a mean of 100 and a
standard deviation of 15. The top 5% of the population have an IQ above what score?
11. Find the following areas of a standard normal distribution.
a. To the left of z = 1.36
c. To the right of z = -0.65
b. Greater than z = 1.28
d. Between z=0 and z =1.54
12. Find the following probabilities of a nonstandard normal distribution with a mean of 86 and standard
deviation of 5.
a. P(x< 80)
c. P( x >92)
b. P(x ≥75)
d. P(85 ≤ x ≤ 95)