Question

SAT Writing Scores are normally distributed with a mean of 493 and a standard deviation of 111.

If 100 students took the SAT, what is the probability their mean test score is higher than 500?

Answer 1

How do I solve this? Would it be \[\frac{ 500-493 }{ 111 }\] =0.06
and then the Z-score=.7257 and since it is higher it would be 1-.7257=.2743.

So my question is, since it is for 100 students would I have to multiply something by 100? Would it be .06? I'm not really sure what to do for that part. Thanks!

Answer 2

Well they ask for the probability of the mean score being higher than 500. This means you should use the distribution for the mean.

The Z-score in question would be \[\frac{500-493}{111/\sqrt{100}} \]

Answer 3

\[\frac{ 500-493 }{ 111/\sqrt{100} }=\frac{ 7 }{ 11.1 }=.63=.7357?\]

Answer 4

0.63 yes. Um the 0.7357 is that the probability you get from the z-score?

Answer 5

yes

Answer 6

Thank you!

Answer 7

Sorry for the delay, I got sidetracked by someone.. Anyway, the question asks
\(P(\bar{X}>500\), which translated with the z-score, becomes
\(P(Z > 0.63)\). However, 0.7357 is for \(P(Z \le 0.63)\). So, you should do \(1-0.7357\)