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This was the question:

A machine fills sacs with sand, of which the mass is normally distributed with µ = 250g, and σ = 20g. If you get a sac of which you know the weight is between 240g and 280g, what's the chance your sac weighs more than 260g?

So I have to calculate $P(X > 260g)$, first I searched the Z-score:

$Z = (x - µ) / σ$

$Z = (260 - 250) / 20$

$Z = 0.5$

Ok, so from what I understood I have to find $P(Z > 0.5)$ in a statistical table, and so I did. I think 0.524 (intersection of 0.30 and infinite) is the closest I can get to 0.5...

But I don't understand, what is now the answer to my question, what is the chance? Is the chance 0.30, or infinite?

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  • $\begingroup$ I think you have to do a condional probability $\mathbb{P}(X>260g \mid 240g<X<280g)$ $\endgroup$
    – Skills
    Jan 27, 2018 at 19:34
  • $\begingroup$ @Skills Thanks for noticing that, but do you also know the answer to my question? $\endgroup$
    – O'Niel
    Jan 27, 2018 at 19:35

1 Answer 1

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If you know the weight is between 240 and 280, then you know that the Z-score is between $-0.5$ and $1.5$. You want to know the probability that, given this information, the Z-score is between $0.5$ and $1.5$: $$ \frac{\Pr[0.5 \le Z \le 1.5]}{\Pr[-0.5 \le Z \le 1.5]}. $$

Begin by getting a table of probabilities instead of the inverse table, where you can look up the numbers you want directly rather than having to search the entire table for them. (Also, you should be looking in a normal distribution table, not a $t$-distribution table.)

This tells us that $\Pr[Z < -0.5] \approx 0.3085$, that $\Pr[Z < 0.5] \approx 0.6915$, and that $\Pr[Z > 1.5] \approx 0.0668$. From there, you should be able to compute the ratio above.

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