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2. Determine whether the following situations would yield a normal distribution. JustifSi
your answer.
a. The results of throwing a die 1000 times
b. The lengths of randomly selected white pine needles
c. The number of people standing in line at five cash registers
3. Sketch a normal curve with a mean of 52 and a standard deviation of 8. Label the x
axis at one, two, and three standard deviations from the mean.
4. The area under the curve of a normal distribution should equal
5. When can the 68-95-99.7 Rule be used? And what is it used for?
6. Use the 68-95-99.7 Rule to state the percentage of values that fall:
(Hint: It may be helpful to draw diagrams for some)
a. Within two standard deviations:
b. Between 0 and 1 deviation above the mean:
c. L4s than 2 deviations below the mean:
d. Betweefl 2 and 3 deviations below the mean:

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7. Assuming the weights of quarters are normally distributed with a mean of 5.67 grams
and a standard deviation of 0.07 grams. Find the following quantities.
a. Percentage of weights more than 5.74 grams
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b. Relative frequency of weights greater than 5.53 grams
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Percentage of weights between 5.81 and 5.53 grams
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d. Relative frequency of weights between 5.46 and 5.74 grams
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8. The lifetimes of light bulbs of a particular type are normally distributed with a mean
of 370 hours and a standard deviation of 5 hours. If 500 light bulbs were tested,
how many would have lifetimes that lie within 1 standard deviation of the
mean?
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9. When a data value is not exactly 1, 2, or 3 deviations from the mean, what must you
do in order to find the percentage of values that fall below that value?
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10. A set of data has a mean of 50 and a standard deviation of 4. Find the z-score of the
value-&7.
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11. Using #10, determine what percentile is7 in.
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12. The amount of Jen’s monthly phone bill is normally distributed with a mean of $50
and a standard deviation of $10. Find the dollar value that corresponds to the 25 th
percentile.
13. At one college, GPA’ s are normally distributed with a mean of 3 and a standard
deviation of 0.6.Find the GPA that corresponds to the 80th percentile.
11, Assume that the income distribution for assembly line workers at a large
manufacturing company is nearly normal with a mean of $ 31,250 and a standard
deviation of$ 6,050. Estimate the percentage of workers who earn between $25,000
and $ 35,000.
14. What are the characteristics of The Central Limit Theore ido>u use the
C.L.T.?
t5. The heights of a large populations of students have a mean of 66” with a standard
deviation of 4”. What is the mean of the distribution of sample means for samples
of 16 students?
t6. The mean salary of the 9,000 em5Ioyees at Holley.com is p = $26,400 with a
standard deviation of o $2. 420. What is the sample standard deviation (Si) for a
random sample of 400 employees?

17. A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume
that a random sample of 24 students is selected and the mean test score of the
sample is computed. What percentage ofsans are less than 70?
18. The mean score on a dexterity test for 12 year olds isp = 30. The standard
deviation is 5. If a psychologist administers the test to a class of 22 students, what
are the chances that the mean of the sj1e is between 27 and 31?