DAT Math destroyer Test 15 number 35 help

[HL86]

Assume that the scores on an entrance exam to collegeville are normally distributed with a mean of 70 and a standard deviation of 8. To earn a scholarship a student's score needs to be on the top 2.5%. What is the minimum score that will guarantee a scholarship?

The answer is 86
The solution says: To be the top 2.5% the score should be 2 standard deviations above the mean. 70+8+8=86

I never took statistics, and I don't understand the solution. Can somebody explain this to me?

Thank you.

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[zEkii]

Our minds aren't equipped to this anymore. Transfer this to the DAT section of the forums.

 

[Incis0r]

Assume that the scores on an entrance exam to collegeville are normally distributed with a mean of 70 and a standard deviation of 8. To earn a scholarship a student's score needs to be on the top 2.5%. What is the minimum score that will guarantee a scholarship?

The answer is 86
The solution says: To be the top 2.5% the score should be 2 standard deviations above the mean. 70+8+8=86

I never took statistics, and I don't understand the solution. Can somebody explain this to me?

Thank you.

Remember the empirical rule for a normal distribution....68-95-99.7.

This diagram may help:

68% falls within 1 standard deviation of the mean (34% above, 34% below).
95% falls within 2 standard deviations of the mean.
99.7% falls within 3 standard deviations of the mean.

You want to be in the top 2.5%, which means you want to be ABOVE 2 standard deviations of the mean.

So the answer is 70 + 2(8)= 86.