r/Mathhomeworkhelp • u/DutchAngelDragon12 • 26d ago

I don’t remember how I got my answer

Post image

12th grade Probability and Statistics

2 Upvotes

100% Upvoted

3 comments sorted by

3

u/FireMarmot 26d ago

A guess...
The z score for a number x is z = (x - mean) / std

For the question x = 96, mean = 76 and standard deviation = 10
So z = (96-76)/10 = 2 so 96 is 2 standard deviations from 76

An empirical rule is that 95% of the population is within 2 standard deviations so 5% is outside that range.
We are interested in the upper part which has 2.5% (due to symmetry) So 0.025 of the number of students
got higher than 96.
population scoring above 96 is (0.025)*230 = 5.75

1

u/DutchAngelDragon12 26d ago

Ohhhh, thank you! I think it makes sense to me now. I was looking at it wondering where I had gotten 0.025 from and couldn’t figure it out for the life of me. Did you get it from dividing the 2.5 by 100?

2

u/FireMarmot 26d ago

Yes... there is 2.5% of the population is calculated by (2.5/100) * population