## anonymous one year ago 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!!!

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1. amistre64

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

2. amistre64

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

3. anonymous

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?

4. amistre64

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.

5. amistre64

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

6. amistre64

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 $x=z(std~dev)+mean$

7. anonymous

ok so right now i got x=z(2.65)+25.3 how would i solve that?

8. amistre64

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

9. amistre64

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

10. amistre64

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. |dw:1442165847068:dw|