Question

Five different size AA batteries of a certain brand were each put into a toy train and the number of minutes the train ran was recorded. The data is shown in the table below. Sketch a normal quantile plot of the data and use it to determine if it is reasonable to assume that the life span of these batteries has a normal distribution.

624

647

658

682

724

Answer 1

Here in this scenario it is given that Five different size AA batteries of a certain brand were each put into a toy train and the number of minutes the train ran was recorded.

From the given data we have to verify weather the life span of these batteries normally distributed.

624

647

658

682

724

Using the normal probability plot we can conclude.

The normal probability plot is computed using following steps,

The sample size is n=5. The following table shows the sample data provided, sorted in ascending order. Also, the theoretical frequencies fi are computed as well as the associated z-scores zi, for i = 1, 2, ..., 5i=1,2,...,5:

Position (i)	X (Asc. Order)	fi	zi
1	624	0.119	-1.18
2	647	0.3095	-0.497
3	658	0.5	0
4	682	0.6905	0.497
5	724	0.881	1.18

Observe that the theoretical frequencies fi are approximated using the following formula:

Now this is the normal probability plot.

From the Normal probability plot we can easily see that the data is linear in pattern i.e 45°. So we can easily conclude that the life span of batteries is normally distributed.

Thank you.