Chapter 6: Q. 35 (page 386)

Suppose $X ~ N (- 3, 1) .$ Between what $x$ values does $95.45 %$ of the data lie? The range of $x$ values is centered at the mean of the distribution(i.e., –3).

Short Answer

Expert verified

The $95.45 %$ of data lies between $(- 5, - 1)$

Step by step solution

Given Information

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

We have to find between what $x$ values does $95.45 %$ of the data lie?

Explanation

According to the empirical rule of normal distribution, approximately $95 %$ values $x$ lies within two standard deviation of the mean.

Therefore, $95.45 %$ of data also will lie approximately near to within two standard deviation of the mean.

From the information given in the question, the random variable $x$ follows normal distribution with parameter $(- 3, 1)$

Hence, the range of $x$ values can be compute as follow:

$= μ \pm 2 σ$

$= - 3 \pm 2 \times 1$

$= - 3 \pm 2$

$= (- 5, - 1)$

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Suppose $X ~ N (- 3, 1) .$ Between what $x$ values does $95.45 %$ of the data lie? The range of $x$ values is centered at the mean of the distribution(i.e., –3).

Short Answer

Step by step solution

Given Information

Explanation

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SupposeX~N(–3,1).Between what xvalues does 95.45%of the data lie? The range of xvalues is centered at the mean of the distribution(i.e., –3).

Short Answer

Step by step solution

Given Information

Explanation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Decision Maths

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Theoretical and Mathematical Physics

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Suppose $X ~ N (- 3, 1) .$ Between what $x$ values does $95.45 %$ of the data lie? The range of $x$ values is centered at the mean of the distribution(i.e., –3).