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Chapter 6: Q. 58 (page 392)

Essay errors : Refer to Exercise 50.

Assume that the number of non-word errors Xand word errors Y in a randomly selected essay are independent random variables. Calculate and interpret the standard deviation of the sumS=X+Y.

Short Answer

Expert verified

The overall number of errors (including word and non-word) ranges by 1.5134 errors on average from the entire mean number of errors, which is 3.1 errors.

Step by step solution

01

Given Information 

Given:

X: the number of non-word errors in a randomly selected essay

Y: the number of word errors in a randomly selected essay

For X:

Mean, μX:2.1errors

Standard deviation , σX:1.136errors

For Y:

Mean, μY:1.0error

Standard deviation, σY:1.0error

02

Calculating and interpreting the standard deviation of the sum S = X + Y.

For both XandY,the total mean of the mean number of errors is:

μx+y=2.1+1.0=3.1errors

The variance of the total is equal to the sum of the variances of the random variables when they are independent.

role="math" localid="1654176907587" σ2X+Y=σ2X+σ2Y=(1.136)2+(1.0)2=2.290496errors

We also know that the standard deviation equals the variance squared:

σX+Y=σ2X+Y=2.290496=1.5134

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