Statistics10010 question

jripper

Ok im having a little difficulty with this question, better to ask then not know it for the exam! Its from the sem 2 2006/07 paper.

Q3a/ At a certain university students are givers z scores instead of the traditional % marks. The mean and standard deviation of the examination percentage sccores are 65% and 15% respectively and it is assumed that the examination results are normally distributed.

i) Any student who scores less than 40% fails their examination. whats is the equivalent zscore needed to pass the exam?

II) what proportion of the students failed the exam?

iii)Using the empirical rule, what percentage scores will 95% of the students score between?

iv) What percentage score would you need to get in this exam so that you would score better than the score of 90% of the sudents in the class?

Do i have to perform some sort of manipulation of this formula: zscore=observed value-mean/standard deviation??

Any info is a great help cheers!

gerry87

jripper wrote: »

Ok im having a little difficulty with this question, better to ask then not know it for the exam! Its from the sem 2 2006/07 paper.

Q3a/ At a certain university students are givers z scores instead of the traditional % marks. The mean and standard deviation of the examination percentage sccores are 65% and 15% respectively and it is assumed that the examination results are normally distributed.

i) Any student who scores less than 40% fails their examination. whats is the equivalent zscore needed to pass the exam?

II) what proportion of the students failed the exam?

iii)Using the empirical rule, what percentage scores will 95% of the students score between?

iv) What percentage score would you need to get in this exam so that you would score better than the score of 90% of the sudents in the class?

Do i have to perform some sort of manipulation of this formula: zscore=observed value-mean/standard deviation??

Any info is a great help cheers!

When you hear 'z-score' you can pretty much think of it as 'Standard Deviations'. So a z-score of 2 is 2 standard deviations.

Mean (X) = 65%
Standard Deviation (s) = 15%

So for i you want to find how many standard deviations below 65% is 40%. Well, 40-65 = 25. So 40% is 25% below 65%, how many standard deviations is this? -25/15 = -1.667, thats your z-score. (That's all just the formula you gave)

What proportion of students, draw your bell curve, put on your z score, colour in the bit you want to find then look up your tables.

95% confidence interval, find your z-score for your 95% confidence interval (remember, two tailed) take the formula you gave in your post and use the z scores you just found. Then work change the formula to find the actual score (i.e. where the 40% was in the formula last time). This is your 95% confidence interval.

The last part is the same as above, the only change is that this time it's only 1 tailed.

WeeBushy

Statistics. *shudders*