Answered: What is the probability that the fuel…

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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Suppose that fuel efficiency (in miles per gallon, mpg) for a particular car model under certain conditions is normally distributed with a mean of 28.0 mpg with a standard deviation of 1.2 mpg. What is the probability that the fuel efficiency for a randomly selected car of this model is between 27 mpg and 31 mpg ?

Convert 31 mpg to a Z SCORE and use it to find the corresponding probability value. Round your answer to the 4th decimal place: __________

Convert 27 mpg to a Z SCORE and use it to find the corresponding probability value. Round your answer to the 4th decimal place:___________

Use the two probabilities to answer the question: What is the probability that the fuel efficiency for a randomly selected car of this model is between 27 mpg and 31 mpg ? Round your answer to the 4th decimal place: _______

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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