Answered: Mopeds (small motorcycles with an…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Mopeds (small motorcycles with an engine capacity
below 50 cm3) are very popular in Europe because of their
mobility, ease of operation, and low cost. The article
“Procedure to Verify the Maximum Speed of Automatic
Transmission Mopeds in Periodic Motor Vehicle
Inspections” (J. of Automobile Engr., 2008: 1615–1623)
described a rolling bench test for determining maximum
vehicle speed. A nor mal distribution with mean value
46.8 km/h and standard deviation 1.75 km/h is postulated.
Consider randomly selecting a single such moped.
a. What is the probability that maximum speed is at
most 50 km/h?
b. What is the probability that maximum speed is at
least 48 km/h?
c. What is the probability that maximum speed differs
from the mean value by at most 1.5 standard deviations?

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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