Question

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1488 and a standard deviation of 292. The local college includes a minimum score of 2014 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement? P(X < 2014) =________ % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1011 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 21.5 and a standard deviation of 3.8. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 49-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.

What would be the equivalent ACT score for this student?
ACT score =
Round answer to 1 decimal place.

If a student gets an SAT score of 1367, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 46 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 46 and 67?


ans = __________%

Answer 1

Q1. Mean 1488, Std Deviation 292 ,

X =2014 , So Z value is = X-mu/sigma = (2014-1488)/292=1.801.

Hence from Normal Distribution P(X<2014)=P(Z<1.801)= 0.964 i.e 96.4% fail to satisfy the admission requirement.

Q2.

As it is assumed that SAT and ACT both measures same aptitute but with different scale , Z value derived from one test can be used for other test as well.

SAT Score : Normal with mean 1011 and std devn 198

ACT Score :  Normal with mean 21.5 and std devn 3.8

a> If SAT Score percentile is 49, Z value is -0.025. Hence SAT Score is 1011-198*0.025 =1006

ACT Score for the same student will be 21.5 -3.8*0.025 = 21.4

For a SAT Score of 1367 , Z value = (1367-1011)/198 = 1.80

Hence ACT Score with Z value 1.80 = 21.5+3.8*1.80=28.3

Q 3. Distribution of Dailty Request follows Normal Distribution with mean 46 and standard Deviation 7 Hence Z values for 46 = 0

and Z values for 67 =( 67-46)/7 = 3

Hence % of request with Z values of 0 and 3 will 49.87% (99.73/2)

Answer : 49.87%