Question

the dotplots show the lifetimes of several brand x and brand y batteries. (a) what percentage of all batteries (both brands together) lasted more than 42 hours? % (round to 2 decimal places).

Explanation:

Step1: Count total number of data - points

Count all the dots in both Brand X and Brand Y dot - plots. There are 5 + 6+ 7+ 4+ 2 (Brand X) + 4+ 3+ 2 (Brand Y)= 33 data - points.

Step2: Count number of data - points with lifetime more than 42 hours

For Brand X, the number of dots at 42, 48, and 54 hours are 7 + 4+ 2 = 13. For Brand Y, the number of dots at 42, 48 hours are 3+ 2 = 5. So, the total number of data - points with lifetime more than 42 hours is 13 + 5= 18.

Step3: Calculate the percentage

Use the formula $\text{Percentage}=\frac{\text{Number of data - points with lifetime}>42}{\text{Total number of data - points}}\times100$. So, $\text{Percentage}=\frac{18}{33}\times100\approx54.55\%$.

Answer:

54.55%