The mean annual income for people in a certain city (in thousands of dollars) is 43, with a standard deviation of 23. A pollster draws a sample of 91 people to interview.(a) What is the probability that the sample mean income is less than 40? Round the answer to at least four decimal places.(b) What is the probability that the sample mean income is between 41 and 44? Round the answer to at least four decimal places.(c) Find the 70th percentile of the sample mean. Round the answer to at least one decimal place.(d) Would it be unusual for the sample mean to be less than 38? Round the answer to at least four decimal places.(e) Do you think it would be unusual for an individual to have an income of less than 38? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.

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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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The mean annual income for people in a certain city (in thousands of dollars) is 43, with a standard deviation of 23. A pollster draws a sample of 91 people to interview.

(a) What is the probability that the sample mean income is less than 40? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean income is between 41 and 44? Round the answer to at least four decimal places.

(d) Would it be unusual for the sample mean to be less than 38? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual to have an income of less than 38? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.

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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Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 24. A pollster draws a sample of 90 people to interview. (c) Find the 60th percentile of the sample mean. Round the answer to at least one decimal place.

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