Consider a set of 7500 scores on a national test whose score is known to be distributed normally with a mean of 510 and a standard deviation of 85. About how many scores greater than 600 would we expect to find?

A. 3750
B. 2664
C. 6414
D. 575
E. 1086

Question

Consider a set of 7500 scores on a national test whose score is known to be distributed normally with a mean of 510 and a standard deviation of 85. About how many scores greater than 600 would we expect to find? 

A. 3750
B. 2664
C. 6414
D. 575
E. 1086

hockeychick23 · Answer

@perl i did 6899/7500 since before you said find the probability of choosing a score greater than 600 but I'm not sure what to do next

perl · Answer

P( X > 600) = P( Z  > ? )

perl · Answer

first lets change the raw score of 600 to a z score

perl · Answer

the z score tells you how many standard deviations away you are from the mean . so how many standard deviations away from the mean is the score of 600 ?

hockeychick23 · Answer

600-510/x= 7500
90/x=7500
x= 83.3

hockeychick23 · Answer

i think i did something wrong finding x

perl · Answer

z = (600 - 510) / 85 will give you the z score

hockeychick23 · Answer

oh sorry thanks, ok so 90/85=1.05882

perl · Answer

so we want P( Z > 1.0588)

hockeychick23 · Answer

i looked it up on the table and got around .8554

perl · Answer

the table gave you the value for P( Z < 1.0588) , so we need to subtract that from 1 to get P( Z > 1.0588)

hockeychick23 · Answer

ok so i got 1-.8554=.1446

perl · Answer

correct

perl · Answer

now multiply that probability by 7500 , to get how many you expect to score more than 600

hockeychick23 · Answer

ok when i did that i got 1084.5 which is close to one of my answers 1086

hockeychick23 · Answer

thanks!(: