Answered: Company A joined a concrete cylinder…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 2GP

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Company A joined a concrete cylinder contest. The strength of their concrete cylinder is normally distributed with mean 80 and standard deviation of 20 kips.

The judging day of the contest arrives and 20 companies have joined. The strength of the concrete cylinders will be tested using a certain machine and it has been decided that company A will be tested last. The 2 highest scores so far are 100 and 70 kips.

1) Determine the probability that company A will be the second place winner.
2) Imagine that company A's cylinder is tested, and it has not shown any sign of distress at a load of 90 kips. Determine the probability that company A will win first place.
3) Company A sent a similar cylinder to another contest. Company B also joined that other contest and their cylinder's strength is expected to be 1% higher than Company A, however their coefficient of variation is 50% higher. Who is more likely to win in this contest?

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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