Math 1342 Exam 3 Review
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1)
For a normal distribution curve with a mean of 9 and a standard deviation of 5,
which of the following ranges of the variable will define an area under the curve
corresponding to a probability of approximately 34%?
1)
2)
Find the area under the standard normal curve that lies between z = -1.9 and
z = 2.2.
2)
3)
Find the probability P(0 < z < 1.67), using the standard normal distribution.
3)
4)
Find the probability P(z > 0.78) using the standard normal distribution.
4)
5)
Find the z value that corresponds to the given area.
5)
6)
A normal population has a mean μ = 28 and standard deviation σ = 5. What
proportion of the population is less than 23?
6)
7)
A bottler of drinking water fills plastic bottles with a mean volume of 999
milliliters (mL) and standard deviation 5 mL. The fill volumes are normally
distributed. What proportion of bottles have volumes between 992 mL and
998 mL?
7)
8)
The average length of crocodiles in a swamp is 11.5 feet. If the lengths are
normally distributed with a standard deviation of 1.7 feet, find the probability
that a crocodile is more than 11 feet long.
8)
9)
Mrs. Smith's reading class can read an average of 175 words per minute with a
standard deviation of 20 words per minute. The top 3% of the class is to receive
a special award. What is the minimum number of words per minute a student
would need to read in order to get the award? Assume the data is normally
distributed.
9)
1
10) In
order to have the standard error of the mean be 10, one would need to take
samples from a normally distributed population with a standard
deviation of 50.
10)
11) The
11)
12) The
12)
13) The
13)
14) Use
14)
15) A
15)
16) A
biologist estimates that 70% of the deer in a region carry a certain type of tick.
For a sample of 300 deer selected at random, what is the chance that 216 or
fewer deer have this tick?
16)
the critical value zα/2 needed to construct a(n) 77% confidence interval.
17)
standard deviation of a normal distribution is 20. What is the standard error
of the mean obtained by averaging 225 samples?
mean annual income for people in a certain city (in thousands of dollars) is
43, with a standard deviation of 29. A pollster draws a sample of 41 people to
interview. What is the probability that the sample mean income is less than 42
(thousands of dollars)?
average age of vehicles registered in the United States is 96 months. Assume
the population is normally distributed with a standard deviation of 15 months.
Find the probability that the mean age of a sample of 36 vehicles is between 98
and 100 months?
the normal approximation to the binomial to find that probability for the
specific value of X.
n = 30, p = 0.4, X = 5
gardener buys a package of seeds. Seventy-nine percent of seeds of this type
germinate. The gardener plants 110 seeds. Approximate the probability that 84 or
more seeds germinate.
17) Find
sample of size n = 41 is drawn from a population whose standard deviation is
σ = 12.5. Find the margin of error for a 99% confidence interval for μ.
18) A
18)
19) A
19)
sample of 35 different payroll departments found that employees worked an
average of 240.6 days a year. If the population standard deviation is 18.8 days,
find the 90% confidence interval for the average number of days μ worked by all
employees who are paid through payroll departments.
2
20) A
student looked up the number of years served by 35 of the more than 100
Supreme Court justices. The average number of years served by those 35
justices was 13.8. If the standard deviation of the entire population is 7.3 years,
find the 95% confidence interval for the average number of years served by all
Supreme Court justices.
21) Find tα/2 when
20)
n = 12 for the 95% confidence interval for the mean.
21)
22) A
sample of size n = 11 has a sample mean x = 15.6 and sample standard
deviation s = 2.4. Construct a 95% confidence interval for the population mean μ.
22)
23) A
23)
sample of 125 tobacco smokers who recently completed a new
smoking-cessation program were asked to rate the effectiveness of the program
on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1
corresponding to "completely ineffective". The average rating was 4.1 and the
standard deviation was 4.0.
Construct a 95% confidence interval for the mean score.
24) In
a survey of 290 registered voters, 139 of them wished to see Mayor
Waffleskate lose her next election. Construct a 98% confidence interval for the
proportion of registered voter who want to see Mayor Waffleskate defeated.
24)
25) A
25)
26) A
26)
recent study of 750 internet users in Europe found that 35% of internet users
were women. What is the 95% confidence interval of the true proportion of
women in Europe who use the internet?
report states that 40% of home owners had a vegetable garden. How large a
sample is needed to estimate the true proportion of home owners who have
vegetable gardens to within 4% with 90% confidence?
27) Find
2
2
the values for χ left and χ right when α = .05 and n = 27.
28) What
is the 95% confidence interval for the standard deviation of birth weights at
County General Hospital, if the standard deviation of the last 25 babies born
there was 1.1 pounds?
3
28)
29) Understand the following definitions:
a. Normal Distribution Properties
b. Z-value
c. Central Limit Theorem
d. Standard error of the mean
e. Maximum error estimate
f. Confidence Level of an interval
g. t-distribution
h. Chi-Distribution
29)
4
Answer Key
Testname: MATH 1342 EXAM 3 REVIEW
from 9 to 14
2) 0.9574
3) 45.25%
4) 0.2177
5) 0.57
6) 0.1587
7) 0.3399
8) 0.62
9) 213
10) 25
11) 1.33
12) 0.4129
13) 15.7%
14) 0.20
15) 0.7881
16) 0.794
17) 1.20
18) 5.03
19) 235.4 < μ < 245.8
20) 11.4 < μ < 16.2
21) 2.20
22) 14.0 < μ < 17.2
23) 3.4 < μ < 4.8
24) 0.411 < p < 0.548
25) 0.316 < p < 0.384
26) 409
27) 13.844 and 41.923
28) 0.9 < σ < 1.5
1)
29)
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