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Chapter 3: Q. 3.122 (page 123)


The data set has mean15and standard deviation 2. Approximately what percentage of the observations lie between 13and 17?

Short Answer

Expert verified

The percentage of the observations lie between 13and 17is68%

Step by step solution

01

Step 1:Given information

We are given that data set has mean15and standard deviation2 .

02

Simplify

We will use empirical rule, to determine approximate values for the percentage of observations between13and17.

We are given that 渭=15and蟽=2, where 渭is mean and 蟽is standard deviation.

Also , the given interval (13,17)will be formed by adding and subtracting standard deviations from the mean.We will check for different values of k.

So using the value of mean and standard deviation , we get , 渭-k蟽,渭+k蟽=(13,17)鈬�k=1

By empirical rule , P渭-蟽<X<渭+蟽鈮�0.68where Xis given interval.

So percentage is68%

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