Math Destroyer question

[jsk26]

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I just started the math destroyer practice test 1 in the 2016 edition. I do not understand the explanation for question 2. The mean=$320 the SD=$20 and we have to find the percentage of people who would pay $280 or less. How do we know that it is 3 SD's? and how can the percentage be determined?

 

[DMikes]

The explanation in the back is pretty thorough....but I guess I'll try to explain it.

The mean is 320, you want less than 280. 280 lies right on 2 SD from the mean since SD = 20 (320 - 280 = 40, 40/20 = 2). You know that 95% of the population falls within 2 SD of the mean. In other words, you know that 95% of people are within 280-360. Therefore, there are 5% of ppl outside of 280-360 and the question explicitly asks for those who are less than 280.

2.5% will be less than 280 and 2.5% will be more than 360 since it is a normal distribution. Your answer is 2.5%

 

[jz123]

1 step. google "statistics normal distribution curve"
2 step. to go from $320 to $280, it takes 2 SD ($40).
3 step. based on the distribution curve, $320-$300 is 34%, $300-$280 is 13.5%, then less than $280 is 2.5%