Download Quiz #2 1) What is the total area under any arbitrary density curve? 1

Probability and Statistics
Quiz #2
Name:
1) What is the total area under any arbitrary density curve?
1
2) Fill in the blanks:
68 % of the observations fall within one standard deviation of the mean.
95 % of the observations fall within two standard deviations of the mean.
99.7 % of the observations fall within three standard deviations of the mean.
3) If X
N ( ; ) ; then what do you have to do to X to get it’s distribution standard normal?
X
4) Given a normal density curve, what is a cumulative proportion at a …xed point z?
The area to the left of z:
5) The distribution of ACT scores for more than 1 million students in a recent high school graduating
class was roughly Normal with mean = 20 and standard deviation = 5: The SAT scores for 1.4 million
students in the same graduating class were roughly Normal with mean = 1000 and standard deviation
= 200:
A) Tonya scores 1300 on the SAT. Jermaine scores 30 on the ACT. Assuming that both tests measure
the same thing, who has the higher score? Report the z scores for both students.
SAT(Tonya):
1300 1000
= 32
200
ACT(Jermaine):
30 20
= 2:
5
Therefore, Jermaine had the higher score.
B) What score on on the SAT is equilvalent to Jermaine’s score from part A)?
1000
2 = x 200
) x 1000 = 400 ) x = 1400:
C) What percentile (i.e. cumulative proportion as a percent) is Tonya’s score from part A)?
By table A;
3
= 93:31%
P Z
2
D) What SAT scores make up the top 15.87% of all scores?
P [Z > z] = :1587 ) P [Z < z] = 1 :1587 = 0:841 3
By table A this means that z = 1:
1000
= 1 ) X 1000 = 200 ) X = 1200:
So, X 200