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Chapter 6: Q. 34 (page 386)

Suppose X~N(15,3). Between what xvalues does 68.27%of the data lie? The range of xvalues is centered at the mean of the distribution (i.e., 15).

Short Answer

Expert verified

The 68.27%of the data lie between (12,18).

Step by step solution

01

Given information

Given in the question that, X~N(15,3)

We have to find between what xvalues does 68.27%of the data lie

02

Explanation 

According to the empirical rule of normal distribution, approximately 68%values xlies within one standard deviation of the mean.

Therefore, 68.27%of data also will lie approximately near to within one standard deviation of the mean.

From the information given in the question, the random variable xfollows normal distribution with parameter (15,3)

Hence, the range of xvalues can be compute as follow:

=μ±lσ

=15±1×3

=15±3

=(12,18)

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