Answer:
a) 6.68th percentile
b) 617.5 points
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:

a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.



has a pvalue of 0.0668
So this student is in the 6.68th percentile.
b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.
He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.




I'd say A. 8000, because you'd get the most answers and the biggest variety in answers for a more accurate sample.
The probability of choosing Joey first is 1/12 .
If that happens, the probability of choosing Chloe next is 1/11 .
Then, the probability of choosing Zoe after that is 1/10 .
The probability of all these things happening is
(1/12) x (1/11) x (1/10)
= 1/1320 = 0.00076 = 0.076 percent
235/4 equals 58.75
Hope this helps!