6. Let the random variable X represent the weight of woman in the U.S., and let

Question

6. Let the random variable X represent the weight of woman in the U.S., and let Y represent the weight of a man. Using the latest Centers for Disease Control (CDC) information we have E(X)s 168.5 pounds, SD(X)-22.5 pounds while E(Y) = 195.7 pounds, SD(Y) = 20.5 pounds Imagine the distribution of choosing two males completely at random, and one female complet measuring their weights and adding the weights up. This creates a new distribution consisting of the sum of three weights as mentioned. ely at random, a. (3] What is the mean of this distribution consisting of the sum of the three weights? Show work/steps, not just the answer, include the use of function notation to communicate what you are doing. Round to two decimal places b. [3] What is the standard deviation consisting of the sum of the three weights? Show work/steps, not just the answer, include the use of function notation to communicate what you are doing. Round to two decimal places

Explanation / Answer

Suppose the mens are Y1 and Y2 from the same distribution Y.

This Implies E(Y1) = E(Y2) = E(Y) = 195.7 pounds

And Also SD(Y1) = SD(Y2) = SD(Y) = 20.5

And One Women is X1 Similarly, E(X1) = E(X) = 168.5 And SD(X1) = SD(X) = 22.5

a) Mean of the Distribution Consisting of Three of sum of the three weights

E(X1+Y1+Y2) = E(X1) + E(Y1) + E(Y2) = 168.5 + 195.7 + 195.7 = 559.9

b) SD of the Distribution Consisting of Three of sum of the three weights

SD(X1+Y1+Y2) = SD(X1) + SD(Y1) + SD(Y2)

= 20.5+22.5+22.5 = 65.5

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.