# Math Help - Help

1. ## Help

I have two questions out of a stat assignment that I just cannot work out (dumb aye?) They are as follows: If there is anyone there that can explain how to work them out in dummy english I would be sooo happy.
Cheers

The probability that a 500mL milk container holds more than 500mL of use is 0.22. If a batch of 10 of these milk containers is tested, what is the probability that:
a) at least half of them will contain more than 500ml?
b) none of them will contain more than 500mL?
(My guess is .5 but thats probably wrong as I cannot figure out how to work it out properly.

Also

Plastic buckets are made by a machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
a) Find Pr(X>1250)
b) Find Pr(1250<X<1380)
c) Find Pr(1135<X<1275)

2. P(x>1250): 1250 is the mean, so it's in the middle of the distribution curve. The portion to the right of the mean is the portion which is greater than 1250. Therefore, 50% is greater than 1250.

P(1250<x<1380): $z=\frac{x-\mu}{\sigma}$

They want the area in between 1250 and 1380. So, using the formula, we find $\frac{1250-1250}{120}=0$. Look up 0 in the z-table. It corresponds to 0.50, as we seen in the previous problem--because it's on the mean. That's why the z-score is 0; The z-score is the number of standard deviations from the mean; So, 1380-1250=130. 120 is 1 standard deviation and this is 130. just a little more. It's 1.08333.....See?. Therefore, it's 1.0833 standard deviations from the mean.

Using the formula and the table, we see that z=1.08 has a prob. of 0.86(in the body of the table).

0.86-0.50=0.36. 36% is between 1250 and 1380.

You do the last one. Okey-doke?.

As far as the first problem goes, are you missing some info?. Say, maybe the number in the sample?

3. Hi Galactus
Thanks so much for replying to my help thread. You definately have helped me.
You are right I had actually left out of the 1st question that it was a sample of 10.

Thanks again
She

4. Originally Posted by she

The probability that a 500mL milk container holds more than 500mL of use is 0.22. If a batch of 10 of these milk containers is tested, what is the probability that:
a) at least half of them will contain more than 500ml?
b) none of them will contain more than 500mL?
(My guess is .5 but thats probably wrong as I cannot figure out how to work it out properly.
>
Given a probability and a sample size so binomial distribution

X ~ B(10, 0.22)

a) At least half is 5 or more

P(X > 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

$P(X = r) = {n\choose r}p^r(1 - p)^{n - r}$

You have p = 0.22 and n = 10

b) Calculate P(X = 0)