Question

The manager of a firm announced: “The lightbulbs produced by our firm have a mean lifetime of 2,500 hours, with a standard deviation of 250 hours; thus, it follows that approximately 95 percent of our lightbulbs last between 2000 and 3,000 hours.”

What was the manager assuming?

What if the assumption did not hold – what percentage of the lightbulbs could you expect would last between 2,000 and 3,000 hours?

Answer 1

Solution:

Given that,

= 2500

= 250

p ( 2000 < x  < 3000 )

= p( 2000 - 2500 / 250 ) ( x -  / ) < ( 3000 - 2500 / 250)

= p ( - 500 / 250 < z < 500 /250 )

= p ( - 2 < z < 2)

= p (z < 2 ) - p ( z < - .2 )

Using z table

= 0.9772 - 0.0228

= 0.9544

Probability = 0.9544 = 95.44%