Question

If a group of data has a mean of 9 and a standard deviation of 2.5, what is the interval that should contain at least 93.8% of the data?

Answer 1

`x=4.325 to x=13.675` interval will contain at least 93.8% of the data.

Explanation:

Mean, SD and area are given.

You must understand `z=(x-barx)/sigma`

We have to find two x values, One is less than mean and another is greater than mean.

Solve the equation for `x`

`x-barx= sigma xx z`

Where `z` is the critical Value. Use the Area under Normal curve to find its value.

Before that find half of the given Probability value. Only for this area or probability value you can get the `z` value.

Half of the Probability value is `93.8/2=46.9 or 0.4690`

`z` value for this is `-1.87` and `1.87`

Substitute these values in the formula and find the range.

Everything is shown in the figure.

Solution to the Problem