6. There is an annual hot dog eating contest in Plattsburg, MS and the average number of hot dogs eaten by one person is 36 with a standard deviation of 6. Find the critical value for a person who can eat more than 2 deviations above the mean.

Question

6.  There is an annual hot dog eating contest in Plattsburg, MS and the average number of hot dogs eaten by one person is 36 with a standard deviation of 6.  Find the critical value for a person who can eat more than 2 deviations above the mean.

kropot72 · Answer

2 standard deviations = 2 * 6 hot dogs
Critical value for more than 2 standard deviations above the mean is:
More than 36 + (2 * 6) hot dogs

anonymous · Answer

So the above mean would be 48?

kropot72 · Answer

Not quite. The critical value is 12 above the mean. Therefore the critical value for more than 2 standard deviations above the mean is the mean (36 hot dogs) + two standard deviations (12 hot dogs) = 48 hot dogs.

anonymous · Answer

So basically to find the answer, I would add together the two standard deviations to get thecritical value, then to find the total number I would add them all together?

anonymous · Answer

not add, I meant multiply the two standard deviations*

kropot72 · Answer

The critical value = two standard deviations + the mean = 48 hot dogs

anonymous · Answer

Okay, thank you so much!

kropot72 · Answer

You're welcome :)

anonymous · Answer

I have one more question. If the question asked: "Find the critical value for a person who can eat less than 2 deviations above the mean." (I added the word "Less"). What would I need  to do then? Would I keep the same formula or would 2 become negative?

kropot72 · Answer

The critical value would remain at 48 hot dogs for both cases. In the first case the person needs to eat more than 48 hot dogs and in the second case the person needs to eat fewer than 48 hot dogs.

anonymous · Answer

Okay, so even if it states it is "less than" it would always remain the same no matter the problem?

kropot72 · Answer

The critical point is a point on the normal distribution curve. The choices are:
(1) on the point
(2) above the point
(3) below the point
In the two cases you are raising 'above the point' means the area of the distribution curve above the critical point and 'below the point' means the area of the distribution curve below the critical point.

anonymous · Answer

Oh okay, I think I understand :)

kropot72 · Answer

I hope that you do understand :)

anonymous · Answer

Here's my last question. 
So if it's below the point the number is lower than the original number, above the point would mean that the number is above the original number, and on the point would mean that the number is the same as the original. Right? :)

kropot72 · Answer

'On the critical value' relates to one specific number of hot dogs. There is a range of possible numbers of hot dogs below the critical value and another range of possible numbers of hot dogs above the critical value.