# Thread: Troublesome standard deviation question

1. ## Troublesome standard deviation question

I am a business student and have a task on standard deviation, I have absolutely no idea how to complete it:

'You and some of your friends from your course are putting on a charity event. Last year different groups raised a mean of £600 with a standard deviation of £120. You want to be in the top 10% of groups this year. Based on last years outcome, how much do you need to raise? Assume money raised followed a normal distribution, use a diagram and show your working'

Any help would be fantastic! Really need saving here.

2. If you want to be in the top 10%, then look up the z-score that corresponds to .9 in the z table. Then, the area to the right of that is the top 10%.

Look at the graph of the normal distribution. The z scores appraoch from the left.

That z score for .90 is approx. 1.28.

$1.28=\frac{x-600}{120}$

$x=753.6$

You need to earn at least 753.6 in order to be in the top 10%.

If you wanted to be in the top 5%, look up the z-score for .95.

Then, we would have $1.645=\frac{x-600}{120}$

$x=797.40$

See now?.

3. I think I am getting there, thank you so so much. When it says draw a diagram, how exactly do i set this out? Do I create this z table that you have used in your answer?

4. Draw the normal curve with the z score labeled at 1.28, along with the 753.6

Then, shade the region to the right of that line.

The z-table is already created and is in most stats books. Inside the front cover, usually.

See, the mean is in the center and is labeled 0. That is your 600.

Then, 1 standard deviation above the mean would be at 600+120=720 pounds.

Yours will be between 1 standard deviation and 2 standard deviations.

Two SD above the mean would be at 600+120+120=840 pounds.

It's actually very easy once you catch on to what it means.

5. You are an absolute life saver! I'm pretty sure its all clicked. Thank you so much. I actually have another question to do about coefficient of variation which I will post once I have got this down, is that ok?

6. One last thing, to get to the 753.6, did you use a sum or actually type in x on your calculator? how do i know that the 1.28 = 753.6?

7. Solve for x:

$1.28=\frac{x-600}{120}$

8. Don't mean to be a pain here but I am really not good with maths basics. How would you actually work out that sum? Do you physically type x-600 in to a calculator, then divide it by 120, to get to the 753.6?