SOLUTION: Please help me Thank you in advance A major credit card company has determined that the amount its customers charge on their accounts is normally distributed with an average of R2

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Question 1125105: Please help me Thank you in advance
A major credit card company has determined that the amount its customers charge on their accounts is normally distributed with an average of R2800 per month and a standard deviation of R200.
2.1) What proportion of customers charge more than R2750 per month on their account (rounded off to three decimals)? [3]
2.2) What percentage of customers charge between R2410 and R3016 per month on their account (rounded off to two decimals)? [5]
2.3) If the company has 20, 000 customers, how many customers charge less than R2430 per month on their account (rounded off to zero decimals)? [2]
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
A major credit card company has determined that the amount its customers charge on their accounts is normally distributed with an average of R2800 per month and a standard deviation of R200.

the mean is 2800 and the standard deviation is 200.

2.1) What proportion of customers charge more than R2750 per month on their account (rounded off to three decimals)? [3]

the proportion of customers that charge more than 2750 per month is .599.

2.2) What percentage of customers charge between R2410 and R3016 per month on their account (rounded off to two decimals)? [5]

the proportion of customers that charge between 2410 and 3016 per month is .83.

2.3) If the company has 20,000 customers, how many customers charge less than R2430 per month on their account (rounded off to zero decimals)? [2]

the proportion of customer who charge less than 2430 is .0322.

with 20,000 customers that comes out to be .0322 * 20,000 = 644.

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the calculator i used can be found at http://davidmlane.com/hyperstat/z_table.html

this is a very nice calculator that takes the drudgery out of finding your answer.

if you need to know how to do it manually, i have some tutorials that might help.

there are other ways to find the answer using technology.

i use the TI-84 Plus Scientific calculator that works good but does require a bit more knowledge on how to use it.

there are also online calculators that work similar to how you would use the z-score tables.

these also require a bit more knowledge but require less more work than using the z-score tables and are a bit more accurate.

i confirmed with the TI-84 Plus that the answer is correct.

if you need lessons on z-scores and how to use them, the following tutorials might be helpful.

https://www.algebra.com/algebra/homework/Probability-and-statistics/change-this-name28108.lesson

https://www.algebra.com/algebra/homework/Probability-and-statistics/THEO-20091109.lesson?content_action=show_source

here's my displays of the use of the online calculator to solve your problem.

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