Question

A light bulb manufacturer wants to advertise a life length interval that excludes no more than 8% of the life lengths on light bulbs of a particular type that she sells. The only information she has is that, for a large number of light bulbs tested, the mean life length was 1500 hours, and the standard deviation was 200 hours. What interval would you suggest? Show your work.

Answer 1

Let T be the life lengths on light bulbs. Then T ~ N(1500, 200)

The life length interval excludes no more than 8% of the life lengths on light bulbs.

Thus, we need to find 100 - 8/2 = 96% confidence interval of life length interval.

Z value for 96% confidence interval is 1.75

96% confidence interval of life length interval is

= (1500 - 1.75 * 200, 1500 + 1.75 * 200)

= (1150, 1850)

Thus the light bulb manufacturer wants to advertise a life length interval of 1150 to 1850 hours.