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Chapter 6: Q. 20 (page 385)

Suppose X~N(4,2). What value of x is two standard deviations to the right of the mean?

Short Answer

Expert verified

The value ofxis two standard deviations to the right of the mean is8.

Step by step solution

01

Given Information 

Given in the question that, X~N(4,2).

We have to find what value of xis two standard deviations to the right of the mean?

02

Explanation 

Let's consider X~N(4,2).

Where,

μ=4

σ=2

From the information given in the question, we observe that the zvalue is 2.

Let's compute the value of zscore:

z=x−μσ

Now, place the provided value in the above equation.

Therefore,

2=x−42

x−4=2×2

x=4+4

x=8

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In the 1992 presidential election, Alaska's 40 election districts averaged 1,956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X=the number of votes for President Clinton for an election district be known.

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