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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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Question content area top

Part 1

An elevator has a placard stating that the maximum capacity is

44004400

lblong dash—2929

passengers. So,

2929

adult male passengers can have a mean weight of up to

4400 divided by 29 equals 152 pounds.4400/29=152 pounds.

Assume that weights of males are normally distributed with a mean of

185 lb185 lb

and a standard deviation of

28 lb28 lb.

a. Find the probability that 1 randomly selected adult male has a weight greater than

152152

lb.

b. Find the probability that a sample of

2929

randomly selected adult males has a mean weight greater than

152152

lb.

c. What do you conclude about the safety of this elevator?

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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