Question

The amount of water in a carton is normally distributed with a mean of 312ml and a standard deviation of 10ml. Every bottle of water is labeled with the serving size as 300 mL.

• What is the probability that a randomly selected carton has less than the labeled serving?
• Determine the amount of water in a carton for which only 2% of cartons fall below this amount.
• Suppose that the water company sells cartons of water as a pack of 24 to supermarket stores. What is the probability that the mean weight of a pack of 24 is in between 305mL and 320mL?

Answer 1

a, Here it is given that distribution is normal with mean=312 and standard deviation is 10

i. We need to find

As distribution is normal we can convert x to z

ii. Here we need to find x such that

Using z table we get

So

Hence

iii. Now as population is normal, as per central limit theorem distribution of sample mean is also normal

We need to find

As distribution is normal we can convert sample mean to z

Answer here is 0.9997