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fabric. 2. The probability distribution of the discrete random variable Y is y 3-у ,y = 0,1,2,3. %D Compute for the mean, variance, and standard deviation of Y.

fabric. 2. The probability distribution of the discrete random variable Y is y 3-у ,y = 0,1,2,3. %D Compute for the mean, variance, and standard deviation of Y.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Quarter 3, Week 2 - Mean, Variance, and Standard Deviation of Discrete Random Variables Performance Task #2 Solve the following problems. 1. The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width is 1 2 3 4 f (x) Find the mean, variance, and standard deviation of imperfections per 10 meters of this fabric. 0.41 0.37 0.16 0.05 0.01 2. The probability distribution of the discrete random variable Y is 3-у FW) = (;)() ,у %3D 0,1,2,3. Compute for the mean, variance, and standard deviation of Y. 3. The local animal shelter adopts out cats and dogs each week with the following probabilities. 3 4 6. 7 8. P(x) 0.15 0.3 0.25 0.18 0.1 0.02 a. Find the mean, variance, and standard deviation for the number of animals adopted each week. b. What is the probability that they find homes for more than 5 animals in a given week? 4. By investing in a particular stock, a person can make a profit in one year of P40000 with probability 0.3 or take a loss of P10000 with probability 0.7. a. What is this person's expected gain/loss? b. Find the variance and standard deviation of this person's expected gain/loss. 5. From experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors. a. Find the mean, variance, and standard deviation for the defective transistors. b. About how many extra transistors per day would the company need to replace the defective ones if it used 10 cartons per day?
Transcribed Image Text:Quarter 3, Week 2 - Mean, Variance, and Standard Deviation of Discrete Random Variables Performance Task #2 Solve the following problems. 1. The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width is 1 2 3 4 f (x) Find the mean, variance, and standard deviation of imperfections per 10 meters of this fabric. 0.41 0.37 0.16 0.05 0.01 2. The probability distribution of the discrete random variable Y is 3-у FW) = (;)() ,у %3D 0,1,2,3. Compute for the mean, variance, and standard deviation of Y. 3. The local animal shelter adopts out cats and dogs each week with the following probabilities. 3 4 6. 7 8. P(x) 0.15 0.3 0.25 0.18 0.1 0.02 a. Find the mean, variance, and standard deviation for the number of animals adopted each week. b. What is the probability that they find homes for more than 5 animals in a given week? 4. By investing in a particular stock, a person can make a profit in one year of P40000 with probability 0.3 or take a loss of P10000 with probability 0.7. a. What is this person's expected gain/loss? b. Find the variance and standard deviation of this person's expected gain/loss. 5. From experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors. a. Find the mean, variance, and standard deviation for the defective transistors. b. About how many extra transistors per day would the company need to replace the defective ones if it used 10 cartons per day?
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