Answered: The annual earnings (in dollars) of 35…

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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A. Find the sample mean
B. Find the sample standard deviation

C. Construct a 98% confidence interval for the population mean

The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data table. Use the data to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 98%
confidence interval for the population mean.
100,107 81,115
77,928
67,923
51,470
67,449 94,660 65,583
78,927
74,311
44,298
86,286
60,460
57,786 55,372 77,728
47,372
98,906
81,344
92,217
63,981
74,412 50,769 60,261
91,316
84,604
79,878 63,741
73,987
57,221 46,863 89,932
74,969 61,333
82,471
(a) Find the sample mean.
(Type an integer or decimal rounded to two decimal places as needed.)

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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