at a high school, the average grade for the english 10 provincial is 64, with a standard deviation of 10. If 20 students scored between 73 and 86 on the exam, how many students took the exam? Use z-score in your solution.

Question

kropot72 · Answer

It must be assumed that the distribution of grades follows the shape of a normal distribution. The normal distibution is that of of a continuous random variable, however in this case the distribution is discrete. Therefore it is necessary to make the correction for continuity when calculating the z-scores.
First you need to calculate the z-scores for 72.5 and 86.5. Can you do that?

anonymous · Answer

ehmm... no

kropot72 · Answer

Have you been taught the following equation to find a z-score?$$z=\frac{X-\mu}{\sigma}$$
If not why are you attempting this question?

anonymous · Answer

=0.9
=2.2

anonymous · Answer

i think

kropot72 · Answer

No, you did not use the X values that I gave you (72.5 and 86.5).

anonymous · Answer

=0.95
=2.25

kropot72 · Answer

Now you need to look up the cumulative probabilities for bo these z-scores and subtract the smaller probability from the larger. This will give the decimal fraction of the total number of students sitting the exam represented by the 20 students.

kropot72 · Answer

Note that you should have calculated 0.85 for the smaller of the two z-scores.

anonymous · Answer

excuse me?

anonymous · Answer

what does  cumulative probabilities mean?

kropot72 · Answer

The table at the following link shows cumulative probabilities for specified z-scores. http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

kropot72 · Answer

Have you recalculated the z-score for 72.5 ?

anonymous · Answer

0.95= .8289
2.25= .9878

kropot72 · Answer

Your cumulative probability result for z = 2.25 is correct. However you are not taking notice of my advice that the z-score for 72.5 is 0.85. You need to find the cumulative probability for a z-score of 0.85 (not 0.95) Can you do that?

anonymous · Answer

0.85=.8023

kropot72 · Answer

Correct. The decimal fraction of the total number of students sitting the exam represented by the 20 students is 0.9878 - 0.8023 = 0.1855.
Therefore the total number of students sitting the exam represented by the 20 students is
$$\frac{20}{0.1855}=you\ can\ calculate$$

anonymous · Answer

=1077.8
so... 108 students?

anonymous · Answer

oops, i meant to say 107.8

anonymous · Answer

is that correct?

kropot72 · Answer

I would use your result of 108 students. Fractional students are not appropriate.

anonymous · Answer

haha, that makes sense, thank you

kropot72 · Answer

You're welcome :)

anonymous · Answer

can you help me with this question also?
determine a 90% confidence interval for μ if  σ=6, x=72, n=81

anonymous · Answer

i don't know what formula to use