Question

In: Math

Below is a list of the top nine longest serving U.S. Supreme Court Justices, along with...

Below is a list of the top nine longest serving U.S. Supreme Court Justices, along with the current Chief Justice of the court:

Name Length of Service (in years)

William O. Douglas 36

Stephen Johnson Field 34

John Paul Stevens 34

John Marshall 34

Hugo Black 34

John Marshall Harlan 33

William J. Brennan 33

Joseph Story 33

James Moore Wayne 32

John Roberts 13

Please provide the following information (1 pt. each):

a. M years of service

b. SD years of service

c. Probability of observing the term length of John Roberts

Expert Solution

a)

The mean for year of service time is obtained using the formula,

Where, X is the length of service time for judges.

From the data values,

Name	Length of Service (in years)
William O. Douglas	36
Stephen Johnson Field	34
John Paul Stevens	34
John Marshall	34
Hugo Black	34
John Marshall Harlan	33
William J. Brennan	33
Joseph Story	33
James Moore Wayne	32
John Roberts	13
Sum	316

b)

The standard deviation for the year of service times is obtained using the formula,

Length of Service (in years), X
36	4.4	19.36
34	2.4	5.76
34	2.4	5.76
34	2.4	5.76
34	2.4	5.76
33	1.4	1.96
33	1.4	1.96
33	1.4	1.96
32	0.4	0.16
13	-18.6	345.96
	Sum	394.4

c)

Let the data values are normally distributed with parameters, mean M and standard deviation, SD.

The probability of obtaining the length of service of John Roberts is obtained by calculating the z score

The probability for z score is obtained in excel using the function =NORM.S.DIST(-2.8097,FALSE)

milcah answered 8 months ago

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