For each question below, sketch a standard Normal curve with your z-value(s) marked on the axis. Show
enough work so that your method can be followed: calculation for z, appropriate shaded area.
1. The scores on the Wechsler Adult Intelligence Scale for 20- to 34-years-olds are, approximately,
normally distributed with mean 100 and standard deviation 20.
a) What percentage of 20- to 34-year-olds are between the intelligence scores of 80 and 120.
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b) What percentage of adults have an IQ score less than 60.
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c) What percentage of adults have an IQ greater than 160.
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Find the percentage of the given z-score.
2. z is less than 1.57
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3. z is greater than -1.17
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Find the percentage of the given z-score.
4. z is between -1.51 and 2.18
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5. z is between 1.22 and 3.21
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6. According to a survey conducted by television advertisers, the average adult American watches an
average of 6.98 hours of television per day. The data is normally distributed with a standard deviation
of 3.80 hours. Find the probability that a randomly selected person watches more than 8.00 hours of
television in a day.
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7. Insurance companies have determined that US males between the ages of 16 and 24, drive an average of
10,718 miles each year with a standard deviation of 3763 miles. Assume the data is normally
distributed. For a randomly selected male in that age group, find the probability that he drives less than
12,000 miles per year.
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8.
The heights of the 880 students at East Meck High School are normally distributed with a mean of 67
inches and a standard deviation of 2.5 inches
a. Draw and label the normal curve.
b. 68% of the students fall between what two heights?
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c. What percent of the students are between 59.5 and 69.5 inches tall?
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d. Approximately how many students are more than 72 inches tall?
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e. If a student is 62 inches tall, how many standard deviations from the mean are they?
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f. If a student is 71 inches tall, how many standard deviations from the mean are they?
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g. If you pick a student at random, what is the probability that they will be between 62 and 72 inches tall?
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h. If you pick a student at random, what is the probability they will be between 65 and 69 inches tall?
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i. What is the probability they will be more than 70 inches tall?
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j. What is the probability they will be less than 61 inches tall?
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9. The heights of six-year old girls are normally distributed with a mean of 117.80 cm and a standard
deviation of 5.52 cm. Find the probability that a randomly selected six-year girl has a height between
117.80 cm and 120.56 cm.
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10. The average heating bill for a residential area is $123 for the month of November with a standard
deviation of $8. If the amounts of the heating bills are normally distributed, find the probability that the
average bill for a randomly selected resident is more than $125.
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11. An IQ test has a mean of 100 with a standard deviation of 15. What is the probability that a randomly
selected adult has an IQ between 85 and 115?
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12. The average adult spends 5 hours per week on a home computer, with a standard deviation of 1 hour.
What percent of adults spend more than 6 hours per week on their home computer?
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13. Draw an example of a normal distribution:
14. The heights of the 1100 students at East Meck High School are normally distributed with a mean of 68
inches and a standard deviation of 1.5 inches.
a. What percent of the students are more than 71 inches tall?
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b. What percent of the students are between 66.5 and 72.5 inches tall?
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15. Find Z if X = 19, μ = 22, and σ = 2.6.
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16. A light bulb advertises that its average (mean) life is 300 hours, with a standard deviation of 20 hours.
a. What is the probability that the light bulb will last less than 250 hours?
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b. What is the probability that the light bulb will last more than 375 hours?
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c. What is the probability that the light bulb will last between 275 and 325 hours?
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17. What are two methods of assessing normality?
__________________________________________________________________________________________
__________________________________________________________________________________________
18. Is the above data normal or skewed? Why?
__________________________________________________________________________________________
19. Students who score in the top 15% on a mathematics admission test at Greenville Tech place out of taking a
college math class. If the average score is 78 with a standard deviation of 6, what is the score that determines if
a student does or does not have to take a college math course?
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20. John finds that there is a scholarship available to all persons scoring in the top 5% on the ACT test. If the
mean score on the ACT is 23 with a standard deviation of 3.7, what score does he need in order to qualify for
the scholarship?
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21. Use the z-score table to find the value of z is less than -0.37.
a) 35.57%
b) 64.43%
c) 22.66%
d) 0.71%
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22. Use the z-score table to find the value of z is greater than 1.58.
a) 5.71%
b) 94.29%
c) 82.38%
d) 1.58%
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