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# Normal distribution question - S2 watch

1. It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
(iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ.
σ = 2.5

Im stuck on how to do this question, i'm not really sure why you go about solving it as P(Z < (750 - μ)/2.5) = 0.02 instead of P(Z < (750 - μ)/2.5) = 0.98? Im also not really sure about why the < sign is used. any help would be appreciated.
2. (Original post by znx)
It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
(iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ.
σ = 2.5

Im stuck on how to do this question, i'm not really sure why you go about solving it as P(Z < (750 - μ)/2.5) = 0.02 instead of P(Z < (750 - μ)/2.5) = 0.98? Im also not really sure about why the < sign is used. any help would be appreciated.
What's the full question?
3. (Original post by znx)
It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
(iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ.
σ = 2.5

Im stuck on how to do this question, i'm not really sure why you go about solving it as P(Z < (750 - μ)/2.5) = 0.02 instead of P(Z < (750 - μ)/2.5) = 0.98? Im also not really sure about why the < sign is used. any help would be appreciated.
Please could you post the full question?

From what I can tell, you are right in saying that P(Z<(750 - μ)/2.5) = 0.02, as 'at least' means you should use the > sign, so P(X>750)=0.98, therefore P(X<750)=1-P(X<750)=0.02, thus P(Z<(750 - μ)/2.5) = 0.02. It's hard to say though since I don't know the full question.

Where did you get the P(Z < (750 - μ)/2.5) = 0.98 from? And what about using the < sign are you confused about?
4. Sorry the full question is:
At a vineyard, the process used to fill bottles with wine is subject to variation. The contents of bottles are
independently Normally distributed with mean μ = 751.4ml and standard deviation σ = 2.5ml.
(i) Find the probability that a randomly selected bottle contains at least 750ml. [3]
(ii) A case of wine consists of 6 bottles. Find the probability that all 6 bottles in a case contain at least 750ml. [2]
(iii) Find the probability that, in a random sample of 25 cases, there are at least 2 cases in which all 6 bottles contain at least 750ml. [4]

It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
(iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ
5. (Original post by gcsemusicsucks)
Please could you post the full question?

From what I can tell, you are right in saying that P(Z<(750 - μ)/2.5) = 0.02, as 'at least' means you should use the > sign, so P(X>750)=0.98, therefore P(X<750)=1-P(X<750)=0.02, thus P(Z<(750 - μ)/2.5) = 0.02. It's hard to say though since I don't know the full question.

Where did you get the P(Z < (750 - μ)/2.5) = 0.98 from? And what about using the < sign are you confused about?
I now know why they used the < sign but when I solve
P(Z > (750 - μ)/2.5) = 0.98, I end up getting the incorrect value of μ.
The answer is μ = 755.1
6. (Original post by znx)
I now know why they used the < sign but when I solve
P(Z > (750 - μ)/2.5) = 0.98, I end up getting the incorrect value of μ.
The answer is μ = 755.1
What value of z are you using?
7. (Original post by old_engineer)
What value of z are you using?
Φ^-1(0.98) which I get a z value of 2.054
8. (Original post by znx)
Φ^-1(0.98) which I get a z value of 2.054
OK there's your problem. You're looking at the wrong part of the bell curve. P(Z > z) = 0.98 is the same as P(Z =< z) = 0.02 and the value of z for which that is true is -2.054, not +2.054.
9. (Original post by old_engineer)
OK there's your problem. You're looking at the wrong part of the bell curve. P(Z > z) = 0.98 is the same as P(Z =< z) = 0.02 and the value of z for which that is true is -2.054, not +2.054.
Thank you that makes more sense now

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