The life expectancy of a typical lightbulb is normally distributed with a mean of 2,000 hours and a standard deviation of 27 hours. What is the probability that a lightbulb will last between 1,975 and 2,050 hours?

Question

anonymous · Answer

0.17619
 0.32381
 0.79165
 0.96784

anonymous · Answer

@Michele_Laino

amistre64 · Answer

what do you ahve to work with, ti83 or tables or what?

anonymous · Answer

what do you mean?

amistre64 · Answer

you have to do calculations, you need something to work them on since im pretty sure you dont want to do an integration of a complicated function ...

what do you have to work it out with?

anonymous · Answer

oh i just have a scientific calculator

amistre64 · Answer

thats not going to do ... unless it has statistical functions built into it.  a ti83 is such a calculator.

amistre64 · Answer

the concept has to do with finding the associated z scores related to the interval in question, and then working out a function, or looking up values in a table

amistre64 · Answer

using the formula:
$$z=\frac{x-mean}{sd}$$
we can determine the z scores for the intervals endpoints.

but then we need a way to find the areas associated with them

michele_laino · Answer

we have  to compute the z-values as @amistre64  well said, in order to that, we have to compute this quantities:
(2000-1975)/27=...?
(2050-2000)/27=...?

anonymous · Answer

0.92
1.85

michele_laino · Answer

now we have to use the table of erf function

amistre64 · Answer

if thats the only recourse we have :)  sure

amistre64 · Answer

-0.92 if the table is left tailing ...

michele_laino · Answer

|dw:1429985368792:dw|
for z=0.92, we have area= 0.3212
for z=1.85, we have 0.4678