Question

Please help~!
Given a test that is normally distributed with a mean of 100 and a standard deviation of 12, find the probability that a sample of 25 scores will have a mean greater than 105.

Show your work so I can understand please! :)

Answer 1

@agent0smith mind if you help?

Answer 2

Ugh sometimes I hate stats. It's easy enough for one test, you just find the z-score and then the probability. But a sample of 25... hmm

Answer 3

I *think* you can do it by using the fact 25 tests, with a mean of 100, should have a
total score of 25*100 = 2500.

The std deviation for the total score of 25 tests would be
sqrt25*12 = 60.

Those come from the properties of st. dev and mean when multiplying them by a constant. I'm tired and don't really feel like explaining them.

And your 25 tests with mean 105 would have a total score
25*105 = 2625

You need P(X > 2625)

Now find the z-score for that \[z = \frac{ 2625 - 2500 }{ 60 } = 2.08 \]
Now finally, use a z-table to find P(z > 2.08)