Answered: Twenty-five percent of all automobiles…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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Question

Twenty-five percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection. (Round your answers to three decimal places.)

(a)

Among 15 randomly selected cars, what is the probability that at most 5 fail the inspection?

(b)

Among 15 randomly selected cars, what is the probability that between 5 and 10 (inclusive) fail to pass inspection?

(c)

Among 25 randomly selected cars, what is the mean value of the number that pass inspection?

Among 25 randomly selected cars, what is the standard deviation of the number that pass inspection?

(d)

What is the probability that among 25 randomly selected cars, the number that pass is within 1 standard deviation of the mean value?

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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