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Chapter 6: Q. 5 (page 409)

Questions T6.5 and T6.6 refer to the following setting. The weight of tomatoes chosen at random from a bin at the farmer鈥檚 market is a random variable with mean 渭=10ounces and standard deviation蟽=1 ounce. Suppose we pick four tomatoes at random from the bin and find their
total weight T.
T6.5. The random variable T has a mean of
(a) 2.5 ounces.
(b) 4ounces.
(c) 10ounces

(d) 40ounces.

(e) 41ounces

Short Answer

Expert verified

The random variable Thas a mean of 40ounces. So, option (d) is correct.

Step by step solution

01

Given information

The weight of tomatoes is a random variable with mean 渭=10ounces and standard deviation 蟽=1 ounce.

02

Explanation

Let,X(one tomato) as:

渭X=10, and 蟽X=1

Then,Tis the random variable for the weight of four tomatoes:

T=X1+X2+X3+X4

The mean and variance (where, XandYare independent):

渭X+Y=渭X+渭Y蟽2X+Y=蟽X2+蟽Y2

The mean and variance of Tis then:

渭T=渭X1+X2+X3+X4=4渭X=4(10)=40

ounces

蟽T2=蟽X1+X2+X3+X42=4蟽X2=412=4ounces2

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