Which Bulb Lasts Longer: Brand A or Brand B?

[rclakmal]

Homework Statement

The life time of electric lights brand A and B independent and normally distributed .For brand A bulbs the mean and standard deviation of the life time are 1010 hours and 5 hours respectively .For brand B those values are 1020 and 10 hours calculate the probability that a Brand A bulb will have a longer life than brand B

Homework Equations

The Attempt at a Solution

If this question was asking about a probability of brand A to have a life time of a particular value (as an example 1000 hours ) then i know how to calculate the probability by converting this distribution to a Standard Normal Distribution by using Z score .then You can easily obtain the value by given tables or by a calculator .That can be also done to brand B.

But the problem is i don't how to connect these two distribution >please someone help on this question .

 

[CompuChip]

When you have two normally distributed variables X and Y you can also form
- a negative -X, with expectation value E(-X) = -E(X) and standarddeviation S(-X) = S(X)
- the sum X + Y, with expectation value E(X + Y) = E(X) + E(Y) and standard deviation S(X + Y) = sqrt( S(X)^2 + S(Y)^2 )

You can use these to see that the difference of the life times is also normally distributed.

 

[rclakmal]

then i should write E(A-B) and S(A-B) as you have mentioned i can obtain values for them.
Then i should consider it as an individual probability .Lets name it as C( C=A-B).
then by tables or by calculator i should obtain a probability value where C>0.

Then i obtain an answer as 0.18555 .Could you please check it and tell me .that would be a great help