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Chapter 6: Q. 35 (page 386)

SupposeX~N(鈥�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., 鈥�3).

Short Answer

Expert verified

The95.45%of data lies between(-5,-1)

Step by step solution

01

Given Information

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

We have to find between what xvalues does 95.45%of the data lie?

02

Explanation 

According to the empirical rule of normal distribution, approximately 95%values xlies 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 xfollows normal distribution with parameter (-3,1)

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

=渭卤2蟽

=鈭�3卤2脳1

=鈭�3卤2

=(鈭�5,鈭�1)

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Most popular questions from this chapter

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

We flip a coin \(100\) times \((n = 100)\) and note that it only comes up heads \(20% (p = 0.20)\) of the time. The mean and standard deviation for the number of times the coin lands on heads is \(\mu=20\) and \(\sigma=4\) (verify the mean and standard deviation). Solve the following:

a. There is about a \(68%\) chance that the number of heads will be somewhere between ___ and ___.

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