Question

A data set has a mean of 58 and a standard deviation of 17. All of the data values are within three standard deviations of the mean. Which of the following could be the minimum and the maximumvalues of the data set?Minimum 5: Maximum 106Minimum 5; Maximum 111Minimum 8: Maximum 111Minimum 2, Maximum 109

Answer 1

To answer this question, we can use the standard normal distribution, and use the z-scores for finding the minimum and maximum values in the distribution.

The z-score is given by:

`z=(x-\mu)/(\sigma)`

We have that the maximum and minimum are within three standard deviations. The z-scores are a measure of the standard deviations from the population mean. Then, the values are for minimum, z = -3, and for maximum, z = 3.

The population's mean is equal to 58 (mu), and the standard deviation is equal to 17.

We are going to find the raw score, x, for the minimum and maximum values 3 standard deviations below and above the mean. Then, we have:

Minimum

`-3=(x-58)/(17)\Rightarrow-3\cdot17=x-58\Rightarrow x=-51+58\Rightarrow x=7`

Maximum