Finding xbar and standard d...

population of 18000.

10% are assigned letter grade of A (given only to those 475+)

80% are letter grade of B (ranges from 25-475)

10% are letter grade of C (25 or less)

Assume normal distribution...

So, I have taken 475-25, div by 2 to get the midpoint of the distribution, which is 225. My text claims the answer is 250 though... I just assumed that with 80% in between 25-475.. the exact mid-point would be halfway between them. **Turns out if its normally distributed, the values are between 0-500.. So it xbar is 250.. but I am still stuck on the SD...

for standard D... I looked at my Z table and took 1.0 value, which is .8413... Subtracted 50% from it(to the left of the mean) leaving with 34.13% of observations between Xbar of 250 and SD... 34.13% of 250 observations is 85.325, which when applied to both sides is 170.65.. book says answer is 175.8

Definitely need help and clarity! Thanks!!