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# S1 Normal distribution watch

1. Need help with this question as I don't know exactly how to calculate a value.

A scientist found that the time taken, M minutes, to carry out an experiment can be modelled by a normal random variable with mean 155 minutes and standard deviation 3.5 minutes.

(c) the value of m, to 1 decimal place, such that P(M ≤ m) = 0.30.

So I know that, P(Z ≤ (m-155)/3.5 = 0.30

But where do I go from there.
2. If the probability of (M <= m) = 0.3,that means that Z is negative doesn't it. So perhaps you need to think about Z=0.7. Then you can find that in the Percentage point of the normal distribution table.

I haven't tried it but what do you think?
3. how do you know its negative from that?
4. And changing it to 0.7 does seem to work but the problem is I looked at the mark scheme and there are additional s.f which I do not understand where they come from.
5. can u please send me a message with the solving pleeeeeeeeeeeeeeeeeeeeease P(-a<Z<a)=0.5820 find the value of a !!
6. (Original post by elfajare)
can u please send me a message with the solving pleeeeeeeeeeeeeeeeeeeeease P(-a<Z<a)=0.5820 find the value of a !!
err sure, we need the mean and the variance as well, the problem should give them.
7. (Original post by Alex Dom)
how do you know its negative from that?
Because the probability is < 0.5 it means the Z is to the left of the mean.
8. You can use symmetry to get and work it from there.
Or you can use your calculator to get for which then
Solve for m and you're done.

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Updated: May 14, 2013
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