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Statistics Help

  • Thread starter ~angel~
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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.
 

Answers and Replies

mezarashi
Homework Helper
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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 ^_^
 
Last edited:
lightgrav
Homework Helper
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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.
 
150
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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?
 

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