Question

For the following set of data, find the percentage of data within 1 population standard deviation of the mean, to the nearest percent. 66,82,69,74,71,74,70,67

Answer 1

We can see that we have some data, and we need to find the mean, and the standard deviation so we can find the normal distribution corresponding to this data.

Therefore, to find the mean, we need to add all of these values and divide the result by the number of values:

Finding the mean of the population

`\begin{gathered} \text{ We can order these values as follows:} \\ \\ 66,67,69,70,71,74,74,82 \\ \\ \mu=(66+67+69+70+71+74+74+82)/(8) \\ \\ \mu=71.625 \\ \end{gathered}`

This is the mean for the given value, μ = 71.625.

Finding the standard deviation for the sample

In this case, we can proceed as follows:

Then we need to add these values and divide them by the number of observations less than 1. After that, we get the square root for the result as follows:

`\begin{gathered} s=\sqrt{(181.875)/(8-1)}=5.09726817591 \\ \\ s=5.09726817591 \end{gathered}`

This is the sample standard deviation for the given values, s = 5.09726817591.

If we assume that the data is the population, the standard deviation will be:

`\begin{gathered} \sigma=\sqrt{(181.875)/(8)}=4.76805778069 \\ \\ \sigma=4.76805778069 \end{gathered}`

Now, we have the parameter for this population: μ = 71.625, σ = 4.76805778069.

To find the per