Question 972837
mean=400, sd=400

z= (x-mean)/sd

a) (2500-2000)/400
z=500/400, or +1.25
Probability more than that is 0.106
b)  (1800-2000)/400
z=-0.5, and want probability to the left
P=0.309

c) From the first two, we have the probability of what we don't want.  Therefore, the probability of what we DO want is the complement of that or 1- the sum of the first two, which add to 0.415.  Therefore, the desired probability is (1-0.415)=0.585

d)The 90th percentile is z=1.282
1.282= (x-2000)/400

Multiply both sides by 400
512.62=(x-2000)
x=2513 people, rounding up, needing an integer for the answer.