Population/Normal distribution

[msierra0290]

A population that is distributed as a normal distribution has a mean of 75 and a standard deviation of 15. This distribution represents a set of tests scores.
a) A person scored 65 on this test. What is the probability that a person selected at random will score 65 or lower?
b)A simple random sample of size 50 is taken from this same population. What is the probability that the sample mean will be 85 or higher?

I have tried this problem for a while now, but math has always been a weakness of mine. Please help

 

[galactus]

A population that is distributed as a normal distribution has a mean of 75 and a standard deviation of 15. This distribution represents a set of tests scores.

a) A person scored 65 on this test. What is the probability that a person selected at random will score 65 or lower?

Just use \(\displaystyle z=\frac{x-{\mu}}{\sigma}\)

Look this value up in the z-table.

b)A simple random sample of size 50 is taken from this same population. What is the probability that the sample mean will be 85 or higher?

Now, use the formula \(\displaystyle z=\frac{(x-{\mu})\sqrt{n}}{\sigma}\)

Look this up in the z-table and subtract from 1.

The reason we subtract here is because it asks for 85 OR HIGHER. The z-table values come from the left and goes right. That is why with the first one we did not have to subtract from 1 because it asks for 65 OR LOWER. Look at a graph of the normal distribution and you can see what I mean.