# Business statistics - variance and mean

The number of items produced in a factory is bell shaped and symmetrical with mean being 50. If variance = 25, what can be said about the proportion of week's production will be between 40 and 60?

This question has me stumped in terms of what it's asking and how to proceed. Any help would be greatly appreciated.

\begin{align} P \left( 40 \leq X \leq 60 \right) &= P \left( \frac{40-50}{\sqrt{25}} \leq Z\leq \frac{60-50}{\sqrt{25}} \right) \\ &= P \left( -2 \leq Z \leq 2 \right) \\ &= \Phi(2) - \Phi(-2)\\ &= 0.9544997 \end{align}

• Perfect. But ... this is a self-study question. The community's policy is to "provide helpful hints" for self-study questions, not solve it. Feb 1, 2017 at 4:44
• @StudentT, thanks. Let me know if you need further hints. Feb 1, 2017 at 4:51
• I'm not the person who ask the question. I just want to mention about the policy here. I was warned by the mods myself before, because I solved someone else's homework. Feb 1, 2017 at 4:52
• Oh. Sorry. I didn't look at the OP's name. Thanks for the advice. Feb 1, 2017 at 4:54

Try to answer the question "what % of the total is between 40 and 60?" Or, "how far from 50 is 40 in terms of variance?" Something like this:

The +1, +2, etc. in the figure is standard deviation, which is the root of variance.

The question is getting at how wide the bell curve is and what that means. It also seems poorly worded. Are you sure you copied the question correctly?

• yeah I made sure to copy down the question exactly (english isn't my teachers first language). What do you mean by "in terms of variance"? 40 and 60 are both 10 away from 50. How does the 25 come into play here? Feb 1, 2017 at 2:43
• The "+1" in the figure is saying one standard deviation (not variance) away from the mean. The standard deviation is the square root of variance, which is 5 for your problem. Feb 1, 2017 at 2:45