My table tells me that the probability of x being more than 1.35 standard deviations from the mean in the positive direction is 0.0885.
Therefore, the answer is
Alternatively, you notice that 300 is 1.35 standard deviations away from 250 and use the table.
There is no way that your instructor is wanting you do know the normal distribution probability density function. That equation pops up in a "upper" lower division stats class, not a stats class for non math majors, which I am guessing this is.
Instead of beating your head against a wall using that equation, why not review your notes on normal distributions and calculating z-scores using a table and a TI83.
This problem should be done in a minute or so after consulting your notes on calculating z-scores (or finding z-scores when given a percentage):
Part A is very simply you plugging 300, 250 and 37 into the equation for a z-score. You should get 1.35. I will leave it to you to interpret the results (after consulting your notes).
Part B is remembering what you learned earlier in the semester about "quartiles" - and that the MIDDLE 50 percent corresponds to the 2 and 3 quartiles, i.e 25% to 75%. Therefore, using your z-chart (in your book, trust me you have one), locate the z-score that applies to .25 percent of the data under a normal curve, and .75 percent of the data under a normal curve. These will give you the z-scores. It is up to you to use the formula for computing a z-score to find the upper and lower bound.
No offense to the other poster, but do not make things more difficult than they are, and take Mr. F's advice and read your notes.