Question

Suppose the wait times at Kroger are 5 minutes with a standard deviation of 2 minutes.

1.  Draw a number line and mark the mean at 5 minutes and mark 1, 2, and 3 standard deviations above and below the mean.  Label the unusual data value range(s) on the number line.
2.  Rosa waits 3 minutes at Kroger.  How many standard deviations from the mean is her wait time?
3.  Binh waits 11 minutes at Kroger.  How many standard deviations from the mean is his wait time?
4.  Is either wait time unusual at Kroger?

Answer 1

Suppose the wait times at Kroger are 5 minutes with a standard deviation of 2 minutes.

1. A number line can be drawn with the mean at 5 minutes, and marks for 1, 2, and 3 standard deviations above and below the mean. The unusual data value range is between 1 and 3 standard deviations from the mean.

   
          -3     -2     -1     0     1     2     3
          |      |      |      |      |      |      |
          |      |      |      |      |      |      |
          |      |      |      |      |      |      |
        -3σ    -2σ    -1σ    μ     1σ    2σ    3σ
   

    

2. Rosa waits 3 minutes at Kroger, which is 0 standard deviations from the mean. This is a typical wait time at Kroger.

3. Binh waits 11 minutes at Kroger, which is 3 standard deviations from the mean. This is an unusual wait time at Kroger, as it is outside of the usual data value range.

4. Binh's wait time is unusual at Kroger, as it is outside of the usual data value range of between 1 and 3 standard deviations from the mean.