A&X Electrical makes a lamp. The Research department found that the life of the lamp is normally distributed with a mean of 5000 hours and a standard deviation of 450 hours.

6. BB Enterprises places a special order from A&X Electrical for 1000 lamps. If their contract states that A&X Electrical will replace all lamps that fail before 4000 hours. How many lamps should A&X Electrical expect to replace?

is this calculated via central limit theorem?

Question

A&X Electrical makes a lamp.  The Research department found that the life of the lamp is normally distributed with a mean of 5000 hours and a standard deviation of 450 hours.

6.	BB Enterprises places a special order from A&X Electrical for 1000 lamps. If their contract states that A&X Electrical will replace all lamps that fail before 4000 hours.  How many lamps should A&X Electrical expect to replace?

is this calculated via central limit theorem?

anonymous · Answer

i got a z value that was way too high doing the central limit theorem.

phi · Answer

what is the z score for 4000  when the mean is 5000 and the std is 450 ?

anonymous · Answer

-2.22

phi · Answer

and what is the Pr(z < -2.22) ?

anonymous · Answer

.0139

phi · Answer

that means the chance of being -2.22 standard deviations below the mean (or in this problem, being a light bulb that lasts less than 4000 hours) is 0.0139
or about 13.9/1000 chance of failing.  Round that to 14/1000 chance of failing.

phi · Answer

The "expected # of failures"  is the probability of failing times the number of bulbs

anonymous · Answer

so 14 bulbs as .0139(1000) is 14 bulbs not including PARTIALS

anonymous · Answer

or rounding up partial bulbs

phi · Answer

It is just an estimate, but we know this much: the answer has to be a whole number because there are no "fractional" bulbs.  The best we can do is either round to the nearest whole integer, or round up to the next biggest integer.  so 14 sounds reasonable.

anonymous · Answer

sounds good to meeeee!