ChapterS Among freshman at a certain university, scores on the Math SAT followed
ID: 3071607 • Letter: C
Question
ChapterS Among freshman at a certain university, scores on the Math SAT followed the normal curve with an averege of 500 and a so of view the normal table (You may "round" z scores and percents to fit the closest line on the normal table and you may round percents on the table to the nearest whole number. 80. Use the normal table to answer the folld and (Put lower number first.) 1. Approximately 68 % of the freshman have SAT scores between Submit Answer Tries o/s 2. Convert a score of 612 to Standard Units (a z score). Submit Answer Tries 0/s 3. What percent of the freshman Math SAT scores are above 6127 Use the z score and the normal table. 12.5 Submit Anseer Tries 3/5 Previous Tries 4. A student with an SAT score of 444 has a z score- Submit Answer Tries 0/5 5. and is in the th percentile. (i.e, what % of the scores are lower than his?) ub Answer Tries 0/5 6. We're going to figure out which SAT score corresponds to the 90 th percentile. First, 90 m/st percentile means 90 % of the area of the histogram is to the left, which leaves a right-hand tail of 10 %. To use our normal table you need to find the MI left-hand tail. To add up to 100% the middle area must be Submit Anwer Tries 0/4 7. Look up the z score for the middle area you just found Sutmit Answer Tries 0/4 8. Now, what SAT score corresponds to the 90 th percentile?Explanation / Answer
1.
Mean = 500
SD = 80
Here' the answer to the question with full concept. Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer
In a normal distribution 68% area under curve is covered 1 deviation from the mean
1 .68% of freshman have SAT scores between 500-80 = 420 and 500+80 = 580
2. 612 into a Z score is X-Mean / Sigma = (612-500)/80 = 1.4
3. This is basically P(X>1.4) = .081 or 8.160%
4. A students with SAT of 444 will have a Z of (444-500)/80 = -.7
5. and is the 24.19th percentile. ( we got this from the Z tables )
6. So, this is 100%-10%-10% = 80% ( 10% each for upper and lower tail)
7. The z score for middle area is 1.282
8. S0, a 90th percentile has a Z score of Z*stdev+Mean = 1.282*500+80 = 721
A score of 721 is basically the 90th percentile.