Answered: The following table shows the number of…

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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Question

The following table shows the number of home runs hit by leaders in the category for the national league during the Zambia Major league Baseball Season. The mean of the data is 37.9 and standard deviation is 11.

B. Demonstrate that one standard deviation around the mean includes 68% of the area under the normal distribution curve.

C. The number of hot dogs sold by a street vendor each day during the same hourlong period is normally distributed, with mean of 31.6 hot dogs and standard deviation of 7.5. Using the empirical rule, identify the range of values around the mean that includes 95% of sales numbers

Sorted National League Home Run Leaders
73
64
57
49
49
45
41
39
38
38
37
37
37
36
36
34
34
34
34
34
33
31
31
30
30
29
27
27
27
25

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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