## anonymous one year ago The scores received by students completing a geology exam are normally distributed. If the average score is 122 and the standard deviation is 35, what percentage of students scored between 52 and 122? (A) 34.0% (B) 37.5% (C) 42.0% (D) 47.5% (E) 48.0%

1. anonymous

2. anonymous

@perl

3. anonymous

@Hero

4. Plasmataco

im bad at these, only 13, but I can try.

5. anonymous

:D

6. anonymous

any help is better than none

7. Plasmataco

dunno. sry

8. ybarrap

$$P(52\le X\le 122)\\ =P(52-\mu\le X-\mu\le 122-\mu)\\ =P(\cfrac{52-\mu}{\sigma}\le \cfrac{X-\mu}{\sigma}\le \cfrac{122-\mu}{\sigma})\\$$ Does this make any sense?

9. ybarrap

This is converting the probability statement into a z-score, a normal random variable with mean 0 and standard deviation 1. This allows us to use the z-table to figure out the probability.

10. ybarrap

$$=P(\cfrac{52-\mu}{\sigma}\le \cfrac{X-\mu}{\sigma}\le \cfrac{122-\mu}{\sigma})\\ =P(-2\le \cfrac{X-\mu}{\sigma}\le 0)\\ =P(0\ge \cfrac{X-\mu}{\sigma}\le 2)\\$$ The last equation follows from symmetry Do you see what we did here?

11. ybarrap
12. ybarrap

This should be sufficient