Finding Probability of Lifetime for Light Bulbs Using Normal Distribution Table

[~angel~]

Note: You'll need the Normal Distribution Table.

A certain type of light bulb has a lifetime in hours which is normally distributed with mean μ=650 and standard deviation σ=40. What is the probablility that a randomly selected light bulb has a lifetime in the range (700, 850)?

Now this is how I tried to do this:

We have to find P(700 ≤ X ≤ 850), but we need it in terms of Z.

Now,
Z= (X-μ)/σ
Z= (X-650)/40

But we have to apply this to all the sides of the inequality, so we end up with

P(1.25 ≤ (X-650)/40 ≤ 5)
= P(1.25 ≤ Z ≤ 5)

But using the Normal Distribution Table, there is no probability for the "5" bit of the inequality. So I'm not sure how to do this.

Thanks.

 

[mezarashi]

Let me explain on how to use the Normal distribution Table. The normal distribution table is... well... normal! It means it has been normalized with a mean of 0 and a standard deviation of 1. To use this standardized table with bell-shaped distributions you get in real life, you need to get the corresponding value of Z. You are in fact stretching/compressing your real life distribution curve accordingly so that it looks like the normal distribution that you do have on the table!

To convert, you have the equation you mentioned
Z= (X-μ)/σ

The subtraction of the mean does the horizontal shift fix, and the dividing by the standard deviation takes care of the fatness/thinness so that they correspond to each other now.

You are looking for a X1=700, and X2=850 right? What does this correspond to on the Z-table? pluggin them in, you will get Z1, and Z2, now you are looking for

P(Z1 ≤ Z ≤ Z2)

which is possible to do ^_^

 

[lightgrav]

A really small table might not go all the way out to z=5.

What do you get from the table at z=3.5?
What do you get from the table at its highest (z= 3.99)?

There's such a small likelihood of finding a bulb with Z>5
that tables ignore the probability of such a miracle bulb.

 

[~angel~]

Thanks for your help, but I can't get the answer. The table goes up to 4 only. I tried your way lightgrav, but it's not right. Is there any other way to work this out?