Question

the life of electric bulbs has a normal distribution with a mean of 35 months and a standard deviation of 4 months. What should the warranty period be if the company that manufactures these bulbs does not want to replace more than 2% of the bulbs?

Answer 1

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.02) and its Z score. Insert the value in the above equation and solve for the score. Remember that the Z score will be negative.

Answer 2

Here mean = 35
s.d.= 4

we have asked that
P(z)=0.98
see normal table
It is z=2.05
remember it is standard normal table value but we have to convert it for x variable for which mean is 35 and s.d. is 4.
do the inverse operation for which we convert x into z.
i.e.
x=mean+z*s.d.
x=35+2.05*4
x=47.3
rounding off it will be 48.

That is answer is 48.