mean/variance

#1
Scores on an examination are normally distributed with mean 75 and variance 22.
a. What is the probability that a student scores 70 or higher?
b. What should be the cutoff point for passing if the instructor wants only the top 20% to pass the exam?
c. Suppose that the instructor gives an A only to the top 10% of the scores. What is the minimum score the student needs to get an A?
 
#2
Hi,

Is it something like this

Problem A

What to find P(x > 70), so we want to find

z =(x -µ)/σ, where x=75, µ=70, and σ =√22 so the z-score should be

z=1.066 or 1.07, look it up on the z-chart and you will that it has a value
of .8577.

Now to find the probability all you have to do is the following,

P(z> 1.07) = (1-.8577) = .1423 or about 14%
Hope this helps for the first portion of your question