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Stat Test 1 Review
1.
In 2007, the monthly rental rates for one bedroom apartments in Ann Arbor, Michigan had a mean of
$700. Suppose those rental rates have approximately a normal distribution, with a standard deviation
of $150. Find the approximate proportion of one-bedroom apartments for which the rental rate
a) is at least $1100 a month.
b) is less than $500 a month.
c) is between $500 and $900 a month.
2.
The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized
measure used in observing infants over time. It is approximately normal with a mean of 100 and a
standard deviation of 16.
a) What proportion of children has MDI of at least 120?
b) What proportion of children has MDI of at least 80?
3.
According to Current Population Reports, self-employed individuals in the United States work and
average of 44.6 hours per week, with a standard deviation of 14.5. If this variable is approximately
normally distributed,
a) what proportion of the self-employed work more than 40 hours per week?
b) what is the probability that a self-employed person’s work hours per week falls between1.75
standard deviations?
4.
Given the frequency distribution below.
x
frequency
1
14
2
3
3
35
4
8
5
12
6
20
7
8
a) Write the probability distribution.
b) Find the mean.
c) Find the standard deviation.
7.
According to the empirical rule for normal distributions, approximately what percent of the data lies
within 3 standard deviations of the mean?
8.
What is the probability that in normally distributed data with a mean of 84.7 and a standard deviation
of 3.12, a value will fall below 72.3?
9.
For each of the following, which curve is wider?
a) curve 1:  = 19,  = 0.7; curve 2:  = 9,  = 0.7
b) curve 1:  = 9,  = 1.1; curve 2:  = 19,  = 1.1
c) curve 1:  = 19,  = 0.7; curve 2:  = 19,  = 1.1
d) curve 1:  = 19,  = 1.1; curve 2:  = 9,  = 0.7
10.
Name the type of sampling method used for each of the following:
a) Students were arranged alphabetically by last name, and every third student was surveyed.
b) A random number generator was used to select 8 numbers from 1 – 30, corresponding to a
numbered class list of students.
c) Students from a class list were first sorted by first letter of last name, and then assigned a number
within each group. One student was randomly selected from each numbered group.
d) Students were separated by age, and all 13-year-old students were surveyed.
11.
Classify each question below as biased or unbiased.
a) Do you actually think classical music is worth listening to?
b) On a weekly basis, do you listen to classical music at least once?
c) Can anyone really like classical music?
d) On a weekly basis, do you listen to ancient, outdated classical music?
12.
A pharmaceutical company has released a new medication to treat heartburn. The company has
designed an experimental study to determine the length of time between taking the medication and
experiencing heartburn relief. The company has resources to monitor 200 total study participants
who suffer from heartburn. Recall that in studies involving medications, placebos are usually
administered as an alternative to the new medication.
a) What are the experimental units of study?
b) What is the explanatory variable?
c) What is the treatment?
d) What is the response variable?
e) Draw a diagram to outline the design of the study.
13.
Find the mean and standard deviation for the
probability histogram.
14.
What is the probability that a number will fall between 14 and 38, given values that are normally
distributed with a mean of 33 and a standard deviation of 1.7?
15a.
Write a probability distribution for the given data.
b.
Find the mean and standard deviation
of the probability distribution.
x
3
4
5
6
7
Freq
72
21
38
43
26
16.
According to the empirical rule for normal distributions, approximately what percent of the data falls
within 2 standard deviations of the mean?
17.
You have normally distributed data with a mean of 115.6 and standard deviation of 6.8.
a) What percent of the values are above 102.4?
b) What percent of the values are below 92.7?
c) What is the probability that a value will be between 112.9 and 121.7?
18.
Find the mean and standard deviation of the data
represented by the probability histogram.