Many cement companies have research and development teams that continuously formulate and experiment different composition of chemicals to fully optimize the cement that they produce. Suppose a research team formulates 5 different mixtures every month. Two mixtures are selected at random from each batch for testing. The possible outcomes of the selection process are represented by pairs. For example, the pair (1, 2) represents the selection of mixtures 1 and 2 for testing. a. List all the different possible outcomes of the selection process. b. Suppose that mixtures 4 and 5 do not meet the requirements of the test. Two mixtures are to be chosen at random. Define ? to be the number of mixtures that does not meet the requirements among those tested. Find the probability distribution of ?. c. Find the cumulative distribution function of ?. Please answer this step by step and justify your answer.
Many cement companies have research and development teams that continuously formulate and experiment different composition of chemicals to fully optimize the cement that they produce. Suppose a research team formulates 5 different mixtures every month. Two mixtures are selected at random from each batch for testing. The possible outcomes of the selection process are represented by pairs. For example, the pair (1, 2) represents the selection of mixtures 1 and 2 for testing. a. List all the different possible outcomes of the selection process. b. Suppose that mixtures 4 and 5 do not meet the requirements of the test. Two mixtures are to be chosen at random. Define ? to be the number of mixtures that does not meet the requirements among those tested. Find the probability distribution of ?. c. Find the cumulative distribution function of ?. Please answer this step by step and justify your answer.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 28PPS
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Many cement companies have research and development teams that continuously formulate and
experiment different composition of chemicals to fully optimize the cement that they produce. Suppose a
research team formulates 5 different mixtures every month. Two mixtures are selected at random from
each batch for testing. The possible outcomes of the selection process are represented by pairs. For
example, the pair (1, 2) represents the selection of mixtures 1 and 2 for testing.
a. List all the different possible outcomes of the selection process.
b. Suppose that mixtures 4 and 5 do not meet the requirements of the test. Two mixtures are to be
chosen at random. Define ? to be the number of mixtures that does not meet the requirements
among those tested. Find the probability distribution of ?.
c. Find the cumulative distribution function of ?. Please answer this step by step and justify your answer.
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