Probability John accepted at X University.

[pecintauttaran]

The X University admission exam's results are distributed normally with mean of 500 and standard deviation of 100. If John wants to accepted at X University, his test result should be better than 70% other applicants. John's test result is 585, calculate probability of John accepted at X University.

 

[Dr.Peterson]

Please follow our guidelines by showing what you have tried. We need to see what you know about the normal distribution.

In particular, the problem seems odd to me; at first glance, it looked as if it would just be asking whether his score is above the threshold, but instead it seems to be about the probability that the actual scores of all students will be such that his given score would pass. I would think you would need to know how many other students there are, as actual results would be a sample of the entire pool of possible students. What topic have you been learning?

Also, of course, acceptance is not really based on one exam alone (note the word "should"), so the question is impossible to answer!

 

[pecintauttaran]

Please follow our guidelines by showing what you have tried. We need to see what you know about the normal distribution.

In particular, the problem seems odd to me; at first glance, it looked as if it would just be asking whether his score is above the threshold, but instead it seems to be about the probability that the actual scores of all students will be such that his given score would pass. I would think you would need to know how many other students there are, as actual results would be a sample of the entire pool of possible students. What topic have you been learning?

Also, of course, acceptance is not really based on one exam alone (note the word "should"), so the question is impossible to answer!

[MATH] \begin{align} P(x \geq 580) &= P(z \geq 0.85)\\ &=0.8023 \end{align}[/MATH]
I think that's the probability that John accepted at X University, but I'm not really sure.

 

[Dr.Peterson]

What you found is not [MATH]P(x\ge580)[/MATH], but [MATH]P(x\le585)[/MATH].

That's the probability that a student in this population would get no more than 585; it doesn't take into account the 70% required for acceptance.

What it does tell us is that John did better than about 80% of the applicants, so it would appear that he meets that requirement; so as far as that one criterion is concerned, he seems certain of acceptance. That's why I said the wording is odd; what it is asking for is not really a probability at all.