Practice Exam 3
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California State University, San Marcos *
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119
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Mathematics
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Jan 9, 2024
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Practice Exam #3: Chapters 6 - 8
NAME _____________________________
Math 119
Spring 2023:
Sarmad Youssef
Show all work to receive full credit.
1)
Assume the readings on thermometers are
normally distributed
with a mean of 0
degrees °C
and a standard deviation of 1.00 degrees °C.
Find the probability that a
randomly selected thermometer reads between −2.22
and −0.99
and draw a sketch of the
region.
2)
Assume that adults have IQ scores that are
normally distributed
with a mean of μ=105
and a standard deviation σ=15.
Find the probability that a randomly selected adult has an
IQ between 94
and 116.
3)
The overhead reach distances of adult females are
normally distributed
with a mean of
204 cm and a standard deviation of 8.5 cm.
a.
Find the probability that an individual distance is greater than
216 cm.
b.
Find the probability that the mean for
23 randomly selected distances is greater than
202 cm.
4)
In a Gallup poll of 1011 adults were asked if they consume alcohol beverages, and 64%
of them said that they did.
Construct a 90% confidence interval of the proportion
of
all adults who consume alcohol beverages.
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5)
You have been hired by a college foundation to conduct a survey of graduates.
If you
want to estimate the percentage of graduates who have made a donation to the college
after graduation, then
how many graduates must you survey
if you want 95%
confidence that your percentage has a margin of error of five percentage points.
6)
Listed below are the ages of randomly selected race car drivers.
Construct a 90%
confidence interval estimate of the mean age
of all race car drivers.
32,
32,
33,
33,
41,
29,
38,
32,
33,
23,
27,
45,
52,
29,
25
7)
A sample of 50 earthquakes have a mean depth of 9.808 km.
Construct a 95%
confidence interval of the mean
of all such depths assuming that the population
standard deviation is known to be 5.013 km.
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8)
You want to estimate the mean grade point average of all current college students in the
United States.
How many grade point averages must be obtained so that the sample
mean is within 0.2 of the population mean?
Assume that a 99% confidence level is
desired.
Also, assume that a pilot study showed that the population standard deviation is
estimated to be 0.79.