SOLUTION: In a recent year, the ACT scores for high school students with an A or B grade point average were normally distributed with a mean of 24.2 and a standard deviation of 4.2. A studen

Algebra ->  Probability-and-statistics -> SOLUTION: In a recent year, the ACT scores for high school students with an A or B grade point average were normally distributed with a mean of 24.2 and a standard deviation of 4.2. A studen      Log On


   

Question 1136419: In a recent year, the ACT scores for high school students with an A or B grade point average were normally distributed with a mean of 24.2 and a standard deviation of 4.2. A student with an A or B average who took the ACT during this time is selected.
Find the probability that a student’s ACT score is less than 21 or more than 33.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 24.2 and standard deviation is 4.2.

you can use the following calculator to answer this question.

http://davidmlane.com/hyperstat/z_table.html

your solution will be:

probability that a score is less than 21 is equal to .2231.

the results are shown below:

$$$

probability that a score is greater than 33 is equal to .0181.

the results are shown below:

$$$

if you wanted to solve this using z-scores, you would do the following:

the formula for z-score is z = (x-m)/s

z is the z-score.
x is the raw score.
m is the mean.
s is the standard deviation.

m is 24.2
s is 4.2

when x = 21, the z-score is (21 - 24.2) / 4.2 = -.7619048

when x = 33, the z-score is (33 - 24.2) / 4.2 = 2.095238095.

you would use the same calculator, only you would set the mean to 0 and the standard deviation to 1.

you would get the same answers as before, only this time you are suing the z-score rather than the raw score.

here's the results.

for less than -.761905.

$$$

for greater than 2.095238.

$$$