Normal Distribution

The mean is 27 and 9:00 is 30 minutes of driving, so if she is going to arrive at or after 9:00, that is 3 minutes past the mean. The standard deviation is 2.5, so 3 minutes is 1.2 standard deviations. Looking up +1.25 standard deviation in a normal table or using this normal function calculator, you get that 89.49% of the time she is earlier than 9:00 and 10.51% she is later. (You could just use the calculator straight without calculating the z score, but you probably need to understand the procedure.) Multiple 10.51% by 200 to get the answer.

"Solution: Given condition n²=(m+1)^3-m^3
n²=3m²+3m+1
and condition 2n+79=m²
let (2n+1)(2n-1)=4n²-1
=12m²+12m+3
3(2m+1)²
since (2n+1)&(2n-1) are odd and their difference is 2, the are relatively prime
We cannot have (2n-1)be three times a square, for then (2n+1) would be a square congruent to 2 modulo 3, which is impossible.

Thus (2n-1) is a square, say b². But (2n+79) is also a square, say a². Then (a+1)(a-1)=a²-b²=80. Since a+b and a-b have the same parity and their product is even, they are both even. To maximize n, it suffices to maximize 2b=(a+b)(a-b) and check that this yields an integral value for m. This occurs when a+b=40 and a-b=2 , that is, when a=21 and b=19. This yields n=181."