# Normally distributed with a mean of 30,000 and sd of 3000. How much newspaper should the Daily Express print so that it has only 5% likely run out?Daily Express is a news editor which tries to...

Normally distributed with a mean of 30,000 and sd of 3000. How much newspaper should the Daily Express print so that it has only 5% likely run out?

Daily Express is a news editor which tries to meet demand and avoid running out of prrinted papers.

*print*Print*list*Cite

### 2 Answers

We are given `mu=30000,sigma=3000` . We want to find an x such that 95% of the demands are less than x.

Assuming the demand is normally distributed:

The z-score that has 95% of all scores to the left is 1.65 from the standard normal table. (Some texts/instructors will use 1.64, others 1.645; yet others may have you interpolate or use technology -- my calculator gives 1.64485)

The formula for z is `z=(x-mu)/sigma` ; solving for x we get `x=z*sigma+mu`

--------------------------------------------------------------------

**The paper should print `x=1.65(3000)+30000=34950` papers to be 95% sure that they will not run out.**

-------------------------------------------------------------------

**Sources:**

How about another case that we want to find an x such that 95% of the demand are more than x( x is on the left hand side of the distribution). Would it be considered as a different case?