Chapter 9 Statistics Worksheet With Answers Page 13
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309.5 Measures of Dispersion
229
( continued )
(
)
(
)
μ
−
2
2
μ
μ
−
−
⋅
x
Class Interval
m
Frequency, f
f
m
x
x
f
i
i
i
i
i
i
i
$24,000−25,999
25,000
83
2,075,000
10,610.0559 112,573,285.48
9,343,582,694.67
$26,000−27,999
27,000
53
1,431,000
12,610.0559 159,013,508.94
8,427,715,973.91
$28,000−29,999
29,000
45
1,305,000
14,610.0559 213,453,732.41
9,605,417,958.24
$30,000−31,999
31,000
36
1,116,000
16,610.0559 275,893,955.87
9,932,182,411.29
$32,000−33,999
33,000
46
1,518,000
18,610.0559 346,334,179.33 15,931,372,249.31
$34,000−35,999
35,000
32
1,120,000
20,610.0559 424,774,402.80 13,592,780,889.49
$36,000−37,999
37,000
6
222,000
22,610.0559 511,214,626.26
3,067,287,757.56
Totals:
1790
25,758,000
147,685,818,994.41
∑
μ
−
2
⋅
(
x
)
f
147, 685,818,994.41
σ
i
i
=
=
≈
9083.28
1790
n
The standard deviation of the tuition is $9083.28.
27. We know that the mean of the IQ test is 100, the
c. Kidneys weighing less than 235 grams or
standard deviation is 15, and the distribution is
more than 415 grams are more than 3 standard
symmetric. So the Empirical Rule applies.
deviations from the mean.
So, 1 – 0.997 = 0.003 or 0.3% of adult male
a. Since 70 is two standard deviations below the
kidneys weigh less than 235 grams or more
mean and 130 is two standard deviations
than 415 grams.
above the mean, the Empirical Rule states that
approximately 95% of the IQ scores are
−
−
325 295
30
385 325
60
=
=
=
= .
between 70 and 130. So we conclude that
d.
1
and
2
30
30
30
30
approximately 95% of persons have an IQ
Since 295 is one standard deviation below the
score between 70 and 130.
mean, and 385 are two standard deviations
b. Since 95% of the scores are between 70 and
above the mean from the Empirical Rule, we
130, 1 – 0.95 = 0.05 = 5% of the scores are
see that 0.34 + 0.34 + 0.135 = 0.815 or 81.5%
either below 70 or above 130.
of the adult male kidneys weight between 295
and 385 grams.
c. Since the Empirical Rule requires the
μ
σ
distribution to be roughly symmetric, we
=
=
31. We are told that
25 and
3.
assume that the percent of scores over 130 is
a. We want the outcome to be between 19 and
equal to the percent below 70. So,
μ
=
−
=
−
=
31, so
k
19 25 19 6,
and
approximately 2.5% of IQ scores are above
according to Chebychev’s theorem, the
130.
probability is at least
29. We are told the distribution of kidney weight is
σ
2
2
3
9
3
bell shaped with a mean of 325 grams and a
−
= −
= −
=
=
1
1
1
0.75.
2
2
standard deviation of 30 grams, so the Empirical
36
4
k
6
Rule applies.
At least 75% of the outcomes are between 19
a. About 95% of kidneys will be between two
and 31.
standard deviations of the mean. That means
b. We want the outcome to be between 20 and
95% of the kidneys will weigh between
μ
=
−
=
−
=
30, so
k
20
25 20 5,
and
325 – 2(30) = 325 – 60 = 265 grams and
according to Chebychev’s theorem, the
325 + 2(30) = 325 + 60 = 385 grams.
probability is at least
−
−
325 235
90
415 325
90
σ
=
=
=
= .
2
2
b.
3
and
3
3
9
16
−
= −
= −
=
=
1
1
1
0.64.
30
30
30
30
2
2
25
25
k
5
According to the Empirical Rule
At least 64% of the outcomes are between 20
approximately 99.7% of the data lie within 3
and 30.
standard deviations of the mean. So,
approximately 99.7% of adult male kidneys
weigh between 235 grams and 415 grams.
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