Question

The total scores on the Medical College Admissions Test (MCAT) in 2013 follow a Normal distribution with mean 25.3 and standard deviation 6.5.
a) what are the median and the first and third quartiles of the MCAT scores? what is the interquartile range?

please i need help!!!

Answer 1

hmm, what properties are you familiar with concerning the normal distribution?

Answer 2

also, how do you define the quartiles? and what do you have to use to do the calculations with?

Answer 3

im familiar with the mean and median
the first quartile is the median of the observations that are to the left of the median
the third quartile is the median of the observations that are to the roiht of the median

i've learned the five number summary. does that help?

Answer 4

in a normal distribution, the measures of central tendency are equal: mean=median=mode.

as far as a quartile goes, I would define it as one-quarter (1/4) of the data.

the first quartile is therefore 25% of the data from the left; the third quartile is 25% of the data from the right.

Answer 5

and the interquartile range is the 50% that lies between them

Answer 6

the hardest part is translating all this into a specific value for the random variable, but there is a formula for that:

\[z=\frac{x-mean}{std~dev}\]

if we know the zscore for our quartiles, then we can solve for x

\[x=z(std~dev)+mean\]

Answer 7

ok so right now i got x=z(2.65)+25.3

how would i solve that?

Answer 8

a table of zscores might help ... or a ti83 or similar calculator to give us the z score of 25%

Answer 9

the inverse normal function ; invnorm(p) ; receives the left tailed probability and outputs the zscore for us.

http://www.wolframalpha.com/input/?i=invnorm%28.25%29

z = +- .675

Answer 10

if you have a table ... you look for the field value closest to .2500 and read the zscore from the row:column it is the intersection of.