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Chapter 6: Q. 36 (page 386)

Suppose X~N(–3,1). Between what xvalues does 34.14%of the data lie?

Short Answer

Expert verified

The 34.14%of data lies between (-3.44,-2.56).

Step by step solution

01

Given Information

Given in the question that, X~N(–3,1).

We have to find between what xvalues does 34.14%of the data lie.

02

Explanation 

The 34.14%is lies in the middle of the normal curve,

Therefore the portion will be divided as equal in both side.

34.14%2=17.07%

So it will be

50%−17.07%=32.93%

So the value of the outside will be32.93%

Now, we need to find the z-value for the 32.93%

z0.3293=−0.44(left−tail)

z0.3293=0.44(right−tail)

The z- score formula is

z=x−μσ

−0.44=x−(−3)1⇒−0.44×1=x+3⇒x=−3−0.44⇒x=−3.44

0.44=x−(−3)1⇒0.44×1=x+3⇒x=−3+0.44⇒x=−2.56

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Use the following information to answer the next four exercises: X~N(54,8)

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