The contents of bottles of water follow a normal distribution with mean μ and standard deviation 4 ml. What proportion of bottles have fill volumes within 1 ml of the mean?

Question

The contents of bottles of water follow a normal distribution with mean μ  and standard deviation 4 ml. What proportion of bottles have fill volumes within 1 ml of the mean?

anonymous · Answer

This could be usefull for you if it is please tick in best response http://answers.yahoo.com/question/index?qid=20101111003300AACEvCt

anonymous · Answer

Nope Id like to know how to get the answer thanks

kropot72 · Answer

The z-scores for the volumes within 1 ml of the mean are as follows:
$$z(\mu +1)=\frac{\mu +1-\mu}{4}=0.25$$
$$z(\mu -1)=\frac{\mu -1-\mu}{4}=-0.25$$
Now you need to find the values of cumulative probability for these two z-scores from a standard normal distribution table. Then subtract the smaller of the two probabilities from the larger to find the required proportion of bottles.