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# Normal Distribution

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1. I'm really struggling with Normal Distribution. I feel that I understand the topic well, however, when questions are put into context I always find myself stomped. Advice?

Question: The heights of a large group of men are normally distributed with a mean of 178 cm and a standard deviation of 4 cm

a) A man is picked at random from the group. Find the probability that he is taller than 185 cm

= 0.0401

b) A manufacturer of door frames wants to ensure that fewer than 0.005 men have to stoop to pass through the framer

2. (Original post by Psst.)
I'm really struggling with Normal Distribution. I feel that I understand the topic well, however, when questions are put into context I always find myself stomped. Advice?

Question: The heights of a large group of men are normally distributed with a mean of 178 cm and a standard deviation of 4 cm

a) A man is picked at random from the group. Find the probability that he is taller than 185 cm

= 0.0401

b) A manufacturer of door frames wants to ensure that fewer than 0.005 men have to stoop to pass through the framer

Convert the context and words into maths and equations. As soon as I see this question, I would write down X ~ N(178, 4^2).

Now, part (a) is just asking me P(X > 185) which is a simple excercise and part (b) is asking me P(X > what?) = 0.005

Well, I know that P(Z > n) = 0.005 if and only if n = 2.5758 (from the tables, what value of Z>z gives a probability of 0.05?)

But we know that n = (what? - 178)/4 and I know that n = 2.5758, so I can just solve for what? now.
3. (Original post by Zacken)
Convert the context and words into maths and equations. As soon as I see this question, I would write down X ~ N(178, 4^2).

Now, part (a) is just asking me P(X > 185) which is a simple excercise and part (b) is asking me P(X > what?) = 0.005

Well, I know that P(Z > n) = 0.005 if and only if n = 2.5758 (from the tables, what value of Z>z gives a probability of 0.05?)

But we know that n = (what? - 178)/4 and I know that n = 2.5758, so I can just solve for what? now.
If the question was given as the part that I made bold in your reply, then everything would be good and I'd be on my way...

The way the question was asked in part a, made it very easy to put into maths. But the second part is a bit more difficult, the only thing I could work out from the second part was that it should = 0.005. How did you work out that it was P(X>...) as opposed to P(X<...)
4. (Original post by Psst.)
If the question was given as the part that I made bold in your reply, then everything would be good and I'd be on my way...

The way the question was asked in part a, made it very easy to put into maths. But the second part is a bit more difficult, the only thing I could work out from the second part was that it should = 0.005. How did you work out that it was P(X>...) as opposed to P(X<...)
It asks for the minimum which kinda forces you to have a X>... since a minimum means that it's the smallest value, not sure I'm putting this across clearly but I think you get the gist? If it's a minimum then any value larger should also work, so X >...

But really, it comes from the context and you learn to spot and understand stuff like this once you've had enough practice translating words into maths.

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