Question

The life expectancy of a typical lightbulb is normally distributed with a mean of 1,975 hours and a standard deviation of 25 hours. What is the probability that a lightbulb will last between 1,950 and 2,050 hours?

Answer 1

Have you considered calculating the Z-Scores?

Answer 2

I got the answer .82. I got it by doing .9772-.1587=.8185. Is that correct?

Answer 3

What were your Z-Scores?

(1975-1950)/25 = 25/25 = +1

And the other?

Answer 4

It was 2 if I remember correctly and I didn't use the z scores

Answer 5

No Z-Score, probably means you were thinking about it strangely. What ws the point of the Normal Distribution? I have a suspicion that you DID, but perhaps were not aware of it.

(2050 - 1950)/25 = 100/25 = 4

That's not very close to 2 in the world of Z-Scores.

Answer 6

So my answer was wrong? I had four answer choices and they were .84, .77, .82, .89

Answer 7

Yes I used wolframalpha. I did (1975-2000)/25 and (2050-2000)/25 and got .9772 and .1587

Answer 8

Brace Yourself. You just calculated Z-Scores!! :-)

P.S. I'm not sure how that first one worked. I hope you mean (1950-1975)/25 and (2050-1975)/25, since 2000 has nothing to do with anything.

Answer 9

Ok awesome :). From (2050-1975)/25 I got .9987 but where does that come in?

Answer 10

Can you tell me if I'm right please? I have a lot of questions left and I could come back later to get the explanation for this one

Answer 11

Part of what you are learning is confidence to realize when you have it right.

0.99865010196837 - 0.158655253931457 = 0.839994848036913

One more time with the empirical rule. Apparently, I'm just making up numbers, today.

1) 1 Standard deviation below the mean cuts off approximately 16% of the probability.
2) 3 Standard deviations above the mean cuts off approximately 99.8% of the probability.

99.8 - 16 = 83.8 -- The empirical rule does a good job when you use the right values.