# Mean or standard deviation?

Which one of mean or standard deviation can used to solve the following problem?

A light bulb is considered defective if it lasts less than 400 hours. The following claim is made:

'Brand A light bulbs are more likely to be defective than Brand B light bulbs.'

Is the claim correct?

$$\begin{array}{c|lc} & \text{} & \text{Mean} & \text{Standard deviation}\\ & Brand A & 450 & 25 \\ & Brand B & 500 & 50 \\ \end{array}$$

My guess is that the claim is incorrect. The reason is that Brand B standard deviation is higher. This shows that although Brand B has a higher mean but the data is more distributed. However I cannot proof my guess. Is there a way that I can find out the number of bulbs that had a higher lifetime of 400, so I can make a comparison?

• See Chebyshev's Inequality and use the fact that 400 is two standard deviations from the mean in both cases. – Austin Mohr Jun 23 '13 at 5:58