Solving Probability Question: Coffee Dispensed in ML per Cup

[thomas49th]

Homework Statement

A drinks machine dispenses coffee into cups. A ign on the machine inicats that each cup contains 50ml of coffee. The machine actually dispenses a mean amount of 55 ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee is normally distributed find

a) the standard deviation of the amount of coffee dispensed per cup in ml.

Homework Equations

The Attempt at a Solution

Well Z ~ N(u,o°)

P(Z < 50) = 0.1

standardise this

$$P(Z < \frac{50-55}{o}) = 0.1$$

So what do I do next. I thought look up the prob distrubution of z = 0.1 in the prob dist tables = 0.5398 but the mark scheme doesn't show this happening at all.

What should I do

Thanks :)

 

[HallsofIvy]

Looks like a good plan to me. But be careful of your numbers. You say you got P(0.1)= .5398 since 50 is less than the mean of 55, $z= (50- 55)/\sigma$ is negative and the probability must be less than 0.50. I suspect you are looking at a table of the normal distribution that only deals with positive values of z. Using the symmetry of the normal distribution, you want $z= (50- 55)/\sigma = .5000- .5398= -.0398$. What is $\sigma$ for that?