Answered: a) Construct a 95% confidence interval…

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) Construct a 95% confidence interval for the population mean, μ Assume the
population has a normal distribution. A sample of 20 part-time workers had mean
annual earnings of $3120 with a standard deviation of $677. Round to the nearest
dollar.
b) Construct a 98% confidence interval for the population mean, μ Assume the
population has a normal distribution. A study of 14 car owners showed that their
average repair bill was $192 with a standard deviation of $8. Round to the nearest
cent.
c) A doctor at a local hospital is interested in estimating the birth weight of infants.
How large a sample must she select if she desires to be 90% confident that her
estimate is within 2 ounces of the true mean? Assume that s = 5 ounces based on
earlier studies.

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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a) Construct a 95% confidence interval for the population mean, μ Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual earnings of $3120 with a standard deviation of $677. Round to the nearest dollar.