Answered: Consider that X1, X2, X3, X4, X5 is an…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Consider that X1, X2, X3, X4, X5 is an independent random sample where Xi follows a normal distribution with a mean of 19 and a variance of 3.2, and Y1, Y2, Y3, Y4, Y5, Y6, Y7 is an independent random sample where Yi follows a normal ̅̅ distribution mean 27 and variance 4.1. Imagine we are interested in the sum of the two sample averages ? + ?. ̅̅ a) What is the mean and variance of ? + ?? Show your work. b) We know that the linear combination of normal random variables has a normal distribution. Using part a, what is the probability the sum of the two samples averages is less than 44?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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