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# S1 Normal distribution finding the probability without a given mean watch

1. The weight, Y grams, of the contents of a tin of ravioli can be modelled by a normal random variable with a mean of m and a standard deviation of 3.0 .Find the value of m such that P(Y < 410) = 0.01

I've looked at the mark scheme for this question and even seen a written solution but I can't understand how to approach the question?

Could someone talk me through this question step by step explaining each step please?

-AmarRPM
2. (Original post by AmarRPM)
The weight, Y grams, of the contents of a tin of ravioli can be modelled by a normal random variable with a mean of m and a standard deviation of 3.0 .Find the value of m such that P(Y < 410) = 0.01

I've looked at the mark scheme for this question and even seen a written solution but I can't understand how to approach the question?

Could someone talk me through this question step by step explaining each step please?

-AmarRPM
If I ask you to find P(Y<y) for some y value, where Y is distributed with mean mu and variance sd^2, how would you find it?
3. (Original post by SeanFM)
If I ask you to find P(Y<y) for some y value, where Y is distributed with mean mu and variance sd^2, how would you find it?
Usually just standardise it and then use the normal distribution tables to get the final answer?
4. (Original post by AmarRPM)
Usually just standardise it and then use the normal distribution tables to get the final answer?
Correct, so how do you standardise it?

(Or if you know that now, how can you solve this question by almost reverse engineering that process?)
5. (Original post by SeanFM)
Correct, so how do you standardise it?

(Or if you know that now, how can you solve this question by almost reverse engineering that process?)
I understand the question a lot better now, but I get the z value as +2.3263, when it seems that I should be getting it as -2.3263.

So basically I'm calculating the mean as -417 when it should be +417. Why is the z value -2.3263 instead of +2.3263?
6. (Original post by AmarRPM)
I understand the question a lot better now, but I get the z value as +2.3263, when it seems that I should be getting it as -2.3263.

So basically I'm calculating the mean as -417 when it should be +417. Why is the z value -2.3263 instead of +2.3263?
Ah yes, well spotted. That is a trap, and there is a clue in the question. If P(Y<410) = 0.01, then is m going to be greater or less than 410? (Think about whether most of the values are going to be to the left of 410 or to to the right - sketch the normal distribution graph, it will probably help)

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