Assume that the standard deviation of monthly rents paid by students in a particular town is $40. A random sample of 100 students was taken to estimate the mean monthly rent paid by the whole student population.What is the standard error of the sample mean monthly rent?What is the probability that the sample mean ex- ceeds the population mean by more than $5?What is the probability that the sample mean ismore than $4 below the population mean?What is the probability that the sample mean differsfrom the population mean by more than $3?

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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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Assume that the standard deviation of monthly rents paid by students in a particular town is $40. A random sample of 100 students was taken to estimate the mean monthly rent paid by the whole student population.

1. What is the standard error of the sample mean monthly rent?
2. What is the probability that the sample mean ex- ceeds the population mean by more than $5?
3. What is the probability that the sample mean is
  
  more than $4 below the population mean?
4. What is the probability that the sample mean differs
  
  from the population mean by more than $3?

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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