1. Recall the Chebyshev' rule. Let X be a random variable with mean u and standard deviation o>0, then for any positive real number k>0 r(x - 2 ka) s or the equivalent P(x - < ka) > 1- 2. Given the following data sets. Data Set I 41 44 45 47 47 48 51 53 58 66 Data Set II 20 37 48 48 49 50 53 61 64 70 The sample mean and sample standard deviation are as follows:

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Could you please solve exercise 3_2 a,b,c

MSc DA DIS 839 _ Assignment 2_2020. ANSWER Sheet - Word
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Exercise 3:
1. Recall the Chebyshev' rule.
Let X be a random variable with mean u and standard deviation o>0, then for any positive real number
k>0
P(x - | 2 ko) s#
or the equivalent
P(x - | < ha) > 1 -
2. Given the following data sets.
Data Set I
41
44
45
47
47
48
51
53
58
66
Data Set II 20
37
48
48
49
50
53 61
64
70
The sample mean and sample standard deviation are as follows:
Data Set I
Data Set II
i = 50.0
s = 14.2
i = 50.0
s = 7.4
a. Which data set has a larger variation? (justify your answer)
b. Is Chebyshev' rule vlerified for these two data sets. (Justify your answer graphically).
c. What can we conclude?
3. In 1903, K. Pearson and A. Lee published the paper "On the Laws of Inheritance in Man. I.
Inheritance of Physical Characters" (Biometrika, Vol. 2, pp. 357-462). The article examined data on
forearm length, in inches, for a sample of 140 men. The mean and standard deviation of the forearm
lengths are 18.8 in. and 1.12 in., respectively.
a. Apply Chebyshev's rule with k = 2 to make pertinent statements about the forearm lengths of
the men in the sample.
b. Repeat part (a) with k = 3.
Page 6 of 10 1435 words
English (United States)
125%
ENG
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Transcribed Image Text:MSc DA DIS 839 _ Assignment 2_2020. ANSWER Sheet - Word budoor alkebsi BA File e Home Insert Draw Design Layout References Mailings Review View Help O Tell me what you want to do A Share X Cut P Find - Cambria (Body - 12 BIU- abe X, x' A A A Aa - A E-E-E-EE H T AaBbCcD AaBbCcD AaBbC AaBbCcC AaB AaBbCcD AaBbCcD AaBbCcD AaBbCcD AABBCCI Copy Paste 1 Normal 1 No Spac. Heading 1 Heading 2 ab Replace D Select * Format Painter Title Subtitle Subtle Em. Emphasis Intense E. Strong Clipboard Font Paragraph Styles Editing 4. S I6. 7. 8 I9. 10. 11I 15. 16 17 18 19 20 Exercise 3: 1. Recall the Chebyshev' rule. Let X be a random variable with mean u and standard deviation o>0, then for any positive real number k>0 P(x - | 2 ko) s# or the equivalent P(x - | < ha) > 1 - 2. Given the following data sets. Data Set I 41 44 45 47 47 48 51 53 58 66 Data Set II 20 37 48 48 49 50 53 61 64 70 The sample mean and sample standard deviation are as follows: Data Set I Data Set II i = 50.0 s = 14.2 i = 50.0 s = 7.4 a. Which data set has a larger variation? (justify your answer) b. Is Chebyshev' rule vlerified for these two data sets. (Justify your answer graphically). c. What can we conclude? 3. In 1903, K. Pearson and A. Lee published the paper "On the Laws of Inheritance in Man. I. Inheritance of Physical Characters" (Biometrika, Vol. 2, pp. 357-462). The article examined data on forearm length, in inches, for a sample of 140 men. The mean and standard deviation of the forearm lengths are 18.8 in. and 1.12 in., respectively. a. Apply Chebyshev's rule with k = 2 to make pertinent statements about the forearm lengths of the men in the sample. b. Repeat part (a) with k = 3. Page 6 of 10 1435 words English (United States) 125% ENG م اكتب هنا ل لبحث
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