(A) If 120 scores are chosen from a normal distribution with mean and standard deviation 8 , how many scores x would be expected to satisfy 67 ≤ x ≤ 83 (B) Usea graphing calculator to generate 120 scores from the normal distribution with mean 75 and standard deviation 8 . Determine the number of scores x such that 67 ≤ x ≤ 83 , and compare your results with the answerto part (A).
(A) If 120 scores are chosen from a normal distribution with mean and standard deviation 8 , how many scores x would be expected to satisfy 67 ≤ x ≤ 83 (B) Usea graphing calculator to generate 120 scores from the normal distribution with mean 75 and standard deviation 8 . Determine the number of scores x such that 67 ≤ x ≤ 83 , and compare your results with the answerto part (A).
Solution Summary: The author calculates the number of scores that satisfies 67le xl 83 if 120 scores are chosen from a normal distribution with mean as 75 and standard deviation as
(A) If
120
scores are chosen from a normal distribution with mean and standard deviation
8
, how many scores
x
would be expected to satisfy
67
≤
x
≤
83
(B) Usea graphing calculator to generate
120
scores from the normal distribution with mean
75
and standard deviation
8
. Determine the number of scores
x
such that
67
≤
x
≤
83
, and compare your results with the answerto part (A).
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
The chart to the right shows that a professor's grading distribution is bell shaped, or normally shaped. The mean of the distribution is 74 and the standard
deviation is 9. Using a Continuous Variable Normal Bell Distribution Model, calculate the minimum test score needed to score in the top 5% of the class.
Complete your work in the worksheet by listing the formula inputs, labels for the formula inputs and make your calculations with formulas. This test problem is
similar to what you studied in video # 32, 33 and 34 and homework problems # 17, 21 and 23.
Relative Frequency
Frequency
Professor looks at all test score for a particular test (this is population
data), and observes:
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Mean = 74
Median = 74
Mode = 73
SD=9
0
0
0 up to 10 up
10
to 20
0
20 up
to 30
0
30 up
to 40
2
40 up
to 50
29
50 up
to 60
X = Score
112
60 up
to 70
225
70 up
to 80
111
80 up
to 90
21
2
90 up 100 up
to 100 to 110
The graph illustrates the distribution of test scores taken by College Algebra students. The maximum
possible score on the test was 140, while the mean score was 74 and the standard deviation was 15.
+
+
29
44
59
74
89
104
119
Distribution of Test Scores
Use the "Empirical Rule", not a calculator or other technology. Do not round your answers.
What is the approximate percentage of students who scored between 74 and 89 on the test?
What is the approximate percentage of students who scored between 44 and 104 on the test?
What is the approximate percentage students who scored between 59 and 89 on the test?
50
What is the approximate percentage of students who scored less than 44 on the test?
, (b) The sum of deviations of a certain number of observations measured from 4 is 72
and the sum of observations of the same value from 7 is –3. Find the number of observations and their
mean.
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Finite Mathematics & Its Applications (12th Edition)
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