Basic Statistics Question

Hi All,

I'm on a few hunting forums, and I understand forum etiquette very well. I would be lying if I said I wasn't looking for some free help here. So if your going to bash a newcomer with a zero post count, stop reading here. I'm a human resources major, so this is very difficult for me... Here is the question.

[FONT=arial, helvetica, sans-serif]The AXIS credit card company is running a promotion where they are going to give a customer a $500 gift card. The company has calculated that the average of all the population charges per month is $2,754 with a standard deviation of $360. The marketing group in AXIS decided that they will randomly select a customer who charges between $3,700 and $3,800 next month. Josh Alivar is the head of the marketing group and wants to get more information about the promotion. Specifically, he wants to know, since the company has 146,886 credit card customers, how many will be eligible to win the gift card?[/FONT]

[FONT=arial, helvetica, sans-serif]I went to our current chapter in my book regarding point estimates and confidence intervals and came up with this. $2,754 +/- 1.96*(360)/(square root of 146,886). I used the z-score of 1.96 and came up with $2,754 +/- 1.84106 for a 95% confidence interval. That is the formula provided by my professor, I'm not really sure how it is applicable. I need to learn how to apply it to finding the number of eligible customers between that $3700 and $3800 mark. Any suggestions? Thank you in advance for any help.[/FONT]

Hey, why should I bash you. I've gone hunting a few times myself.

If the mean is 2754 and the standard deviation is 360 then, since
(3700 - 2754) / 360 ~ 2.63,
3700 is about +2.63 standard deviations from the mean. Similarly, 3800 is about +2.91 standard deviations from the mean. If the credit card charges follow a normal distribution, the probability that the credit card charges will be greater than $3700 is
P(z>2.63) ~ .0043
and the probability that the credit card charges will be greater than $3800 is
P(z>2.91) ~ .0018.
So the probability that the credit card charges will be between $3700 and $3800 is about 0.0043 - 0.0018 = 0.0025. Since there are 146,886 credit card customers and 0.0025 * 146886 ~ 367, one should expect about 367 customers with charges between $3700 and $3800.

Thanks a ton Ishuda!!

That was really simple to follow once it's put in lamen's terms.

Yeah, on lots of various types of forums people are pretty weary of first timers with low post counts coming in hot with their hand out looking for freebies. Thanks again.