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Chapter 6: Q.15 (page 355)

Spell-checking Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X. Show your work

Short Answer

Expert verified

The number of nonword errors is on average 1.1358 words from the mean.

Step by step solution

01

Given Information

The distribution of the number Xof nonword errors is as follows:

02

Explanation

The expected value is calculated by multiplying each possibility by its probability:

E(X)=鈭�xP(x)=0脳0.1+1脳0.2+2脳0.3+3脳0.3+4脳0.1=2.1

The expected value of the squared variation from the mean is the variance:

蟽2=鈭�(x-渭)2P(x)=(0-2.1)2脳0.1+(1-2.1)2脳0.2+(2-2.1)2脳0.3+(3-2.1)2脳0.3+(4-2.1)2脳0.1=1.29

The square root of the variance is the standard deviation:

蟽=蟽2=1.29鈮�1.1358

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