Question

A battery manufacturer is interested in the lifetime of its products. Thirty batteries are tested until they fail. The times to failure (in hours) are given below.

41.3 21.1 35.6 13.5 4.2 15.8
5.5 5.8 33.6 18.6 24.3 18.1
3.5 8.4 42.1 9.4 10.6 8.9
13.7 19.6 9.2 5.9 19.4 24.2
27.3 30.6 29.4 18.0 32.8 15.6

a) Construct a graph to display the data.

Answer 1

Battery lifetimes varied from 4.2 to 42.1 hours. 50% lasted longer than 20 hours, as the manufacturer claimed. Median lifetime was 18.6 hours.

The data in the image shows the battery lifetimes for 30 batteries. The lifetimes range from 4.2 hours to 42.1 hours. The manufacturer claims that 50% of its batteries last longer than 20 hours.

We can construct a cumulative distribution graph to display the data. This graph shows the percentage of batteries that have failed by a certain time.

The graph shows that 50% of the batteries have failed by 20 hours. This is consistent with the manufacturer's claim.

We can also calculate the median lifetime, which is the time at which 50% of the batteries have failed. The median lifetime in this case is 18.6 hours.

The graph can also be used to estimate the lifetime of a particular battery. For example, if you want to know how long 90% of the batteries last, you can find the 90th percentile on the graph. The 90th percentile in this case is 33.6 hours.

In conclusion, the data in the image shows that the battery lifetimes are fairly evenly distributed. The manufacturer's claim that 50% of its batteries last longer than 20 hours is supported by the data. The median lifetime is 18.6 hours, and the 90th percentile is 33.6 hours.