Pre-Calculus - Eduware

VIII. PROBABILITY AND STATISTICS 5. Standard Deviation
1822. The table below shows the age at inauguration of ten
presidents of the United States.
1826. The table below shows the scores on a writing test in an
English class:
Find, to the nearest tenth, the standard deviation of the age
at inauguration of these ten presidents.
7.7
1824. As one of its admissions criteria, a college requires an SAT
math score that is among the top 70% (69.1%) of all scores.
The mean score on the math portion of the SAT is 500 and
the standard deviation is 100. What is the minimum
acceptable score? Justify your answer by drawing a sketch
of the normal distribution and shading the region
representing acceptable scores.
450
1825. In her algebra class, Ms. Goodheart predicts 8 of her 26
students will earn a score of 90 or above on a particular
exam with a normal distribution. After taking the exam, the
mean score was 84 with a standard deviation of 6. Was her
prediction accurate? What should she have predicted to be
more precise?
1829. The scores on a 100 point exam are normally distributed
with a mean of 80 and a standard deviation of 6. A student's
score places him between the 69 th and 70 th percentile.
Which of the following best represents his score?
(1) 66 (3) 84
(2) 81 (4) 86
1832. A group of students that are normally distributed bring an
average of $5.00 with them to school each day with a
standard deviation of $0.50. How much money will 68% of
students bring to school?
(1) $4.25 to $5.25 (3) $4.75 to $5.25
(2) $4.50 to 5.50 (4) $4.00 to $5.00
a Using the accompanying set of data, find both the mean
and the standard deviation to the nearest tenth.
b What is the number of scores that fall within one standard
deviation of the mean?
c Find, to the nearest tenth, the percentage of scores in this
set of data that are within one standard deviation of the
mean?
d What is the number of scores that fall within two standard
deviations of the mean?
e Find the percentage of scores in this set of data that are
within two standard deviations of the mean.
a mean = 79.4 standard deviation = 8.4
b 24 c 66.7% d 34 e 94.4%
1833. On a school exam, Mr. Perez's class had a mean score of 87
and a standard deviation of 11. Mrs. Steck's class had a
mean score of 83 and a standard deviation of 8. In which
class was there greater consistency in the scores? Explain
how you arrived at your answer.
Mrs. Steck's class
Base your answers to questions 1834 and 1835 on the information
below. During school physicals the height of each girl on the
soccer team was taken, in inches, and had the following results:
60, 63, 65, 75, 79, 58, 62, 2, 59, 61, 66
1834. Find, to the nearest tenth, the standard deviation.
6.6 inches
1835. What percent of the girls are between one standard
deviation away from the mean?
72%
1851. The class mean for a math test was 80. The standard
deviation was 8. What percentage of the class scored
between a 76 and 84?
(1) 68.2% (3) 26.4%
(2) 52.8% (4) 38.2%
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