The central limit theorem

[Mahonroy]

Hello, I came across this problem and I wasn't entirely sure on how to do it. I'm pretty sure the central limit theorem needs to be used, just not sure how to set it up. Any help is greatly appreciated, thanks!

 

[galactus]

For the first part, us the formula \(\displaystyle z=\frac{(x-{\mu})\sqrt{n}}{\sigma}\)

\(\displaystyle z=\frac{(30-30.01)\sqrt{50}}{.1}=-.7071\)

Look up the z score and we see the probability is .2398. But we want the probability it is MORE than 30 per barrel.

1-.2398=.7602

About 76%

 

[Mahonroy]

Thanks for the reply! Where does the 1500L come into play?
I guess I'm confused on how to incorporate the total amount in b and c, such as incorporating the 2401L, etc.?

 

[Deleted member 4993]

Thanks for the reply! Where does the 1500L come into play?
I guess I'm confused on how to incorporate the total amount in b and c, such as incorporating the 2401L, etc.?

50 * 30 = 1500