he maximum grade allow for this exam was 128 points. (a) Find the mean and standard deviation of the grades. (b) Person A computed the interval ¯x±2s to be (102.42, 142.18) and claims that this interval contains approximately 95% of the grades. As an expert consultant you have been contacted by investigator B to help confirm her points: i. Investigator B believes that, regardless of the percentage of grades contained in the interval, the interval should be (102.42, 128). Do you agree? Explain in no more than 2 sentences. ii. Investigator B believes that that it is not necessarily true that his interval contains approximately 95% of the grades. Do you agree? Explain in no more than 2 sentences. Grades 128 128 128 128 118 124 128 124 119 128 128 117 117 116 128 121 128 122 124 128 128 128 102 124 128 120 128 128 101 128 125 124 104 94 128 128 128 122 121 122 104 121 122 128 126 128 119 106 128 117 124 128 120 128 124 100 128 128 128 128 124 128 123 124 122 125 128 128 126 128 128 124 128 111 126 124 128 128 128 125 128 101 122 124 120 128 128 107 115 128 127 120 121 128 128 122 126 126 128 125 128 120 128 128 128 128 124 117 128 128 124 109 128 122 128 123 124 124 118 128 128 128 122 60 124 120 124 128 128 99 121 124 125 128 116 128 128 124 124 128 109 128 128 124 116 124 128 118 118 128 124 124 121 125 126 125 122 128 125 128 128 128 101 117 120 106 123 128 108 126 106 128 128 128 128 128 108 128 128 124 124 126 124 125 128 128 125 128 124 128 128 128 104 120 126 128 122 120 128 128 80 68 122 128 128 128 122 124 122 128 128 128 128 128 125 128 128 116 128 116 72

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The maximum grade allow for this exam was 128 points.
(a) Find the mean and standard deviation of the grades.
(b) Person A computed the interval ¯x±2s to be (102.42, 142.18) and claims that this interval contains approximately 95% of the grades. As an expert consultant you have been contacted by investigator B to help confirm her points:
i. Investigator B believes that, regardless of the percentage of grades contained in the interval, the interval should be (102.42, 128). Do you agree? Explain in no more than 2 sentences.
ii. Investigator B believes that that it is not necessarily true that his interval contains approximately 95% of the grades. Do you agree? Explain in no more than 2 sentences.

Grades	128	128	128	128	118	124	128	124	119	128	128	117	117	116	128	121	128
122	124	128	128	128	102	124	128	120	128	128	101	128	125	124	104	94	128
128	128	122	121	122	104	121	122	128	126	128	119	106	128	117	124	128	120
128	124	100	128	128	128	128	124	128	123	124	122	125	128	128	126	128	128
124	128	111	126	124	128	128	128	125	128	101	122	124	120	128	128	107	115
128	127	120	121	128	128	122	126	126	128	125	128	120	128	128	128	128	124
117	128	128	124	109	128	122	128	123	124	124	118	128	128	128	122	60	124
120	124	128	128	99	121	124	125	128	116	128	128	124	124	128	109	128	128
124	116	124	128	118	118	128	124	124	121	125	126	125	122	128	125	128	128
128	101	117	120	106	123	128	108	126	106	128	128	128	128	128	108	128	128
124	124	126	124	125	128	128	125	128	124	128	128	128	104	120	126	128	122
120	128	128	80	68	122	128	128	128	122	124	122	128	128	128	128	128	125
									128	128				116	128	116	72

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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