# Help finding the maximum number of instances.

#### carminevu91

##### New Member
So this is a homework question.

There were 40 chess matches at the World Chess Championships. If we assume that the average attendance for all those games was 750 spectators:

What is the maximum number of games in which there could have been at least 1,500 spectators if the standard deviation of the attendance was 250?

I can plot the data, no problem. I can find the probability, no problem. What I can't seem to find out is *how* to figure the maximum number of games that could have 1,500 spectators, with a standard deviation of 250. I've still got training wheels on my statistical bike, so if anyone could give me a shove in the right direction, I'd very much appreciate it.

EDIT: I did some math, and I could be way off. But it looks like every instance of 1500 spectators (when mean is 750) adds roughly 118 to the standard deviation. So, I *think* the answer might be 2. 2 instances of 1,500 would add 236 to the standard deviation. Though I'm not certain.

Thanks again!

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#### Karabiner

##### TS Contributor
Doesn‘t the question mention the distribution of attendances around the mean, e.g. normal distribution?

With kind regards

Karabiner

#### carminevu91

##### New Member
3. There were 40 chess matches at the World Chess Championships. If we assume that
the average attendance for all those games was 750 spectators:

(a) What is the maximum number of games in which there could have been at least 3,000
spectators?

(b) What is the maximum number of games in which there could have been at least 1,500
spectators if the standard deviation of the attendance was 250?

This is the entirety of the question. (a) has no mean or standard deviation requirements, so it was simply an algebra question. No problem there.

(b) is the one where standard dev *must* be 250. I've played with the numbers to get there. Seems the right answer has to be 2. I just don't know *how* it is 2.

I made a spreadsheet with 40 data points with 30,000 fans, standard deviation 250. And it seems anything over 1,500 occurring more than twice pushes the standard deviation above 250.

So I think I have the answer. Though my stats professor probably isn't going to accept "I plugged numbers into a spreadsheet for 90 minutes until I made the numbers work" as 'showing my work.'

Thanks again!

#### carminevu91

##### New Member
Doesn‘t the question mention the distribution of attendances around the mean, e.g. normal distribution?

With kind regards

Karabiner

I think it has to be normal distribution. That's all we've covered so far.

Thanks!

#### carminevu91

##### New Member
I think I might have stumbled across the answer.

The probability of a game having at least 1,500 spectators is .0013. Over 40 games that's .0052. Meaning the maximum number of games with at least 1,500 (standard deviation of 250) is 1.

I think that's right. Fingers crossed.