Answered: In an upstate county in New York state,…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

In an upstate county in New York state, county administration did a statical study on household electricity bills. The electricity bills are approximately normally distributed with a mean of $200 and a standard deviation of $33. A county clerk selected a random sample 36 electricity bills for this study.

a. Using this information, compute the mean of the sampling distribution of mean for samples of size 36?

b. What is the standard error of the sampling distribution of mean for samples of size 36?

c. If the sample mean of the above sample is $194, what is the z-score that represents the location of this value in the sampling distribution? (round to two decimal places)

d. What is the probability of getting a sample mean of 36 bills is less than $194? (round to four decimal places)

e. What is the 95th percentile of sampling distribution of mean for samples of 36 bills? (round your answer to a whole number)

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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