Download N S I Open separ Obtai probl Part The p devia 1 2 3 4 Part The p

ATHSFC– MathDepa
artmentAl Ain(2013‐2014)
SWQWorrksheet(TeermI)
Grade1
11APStatisstics
N
Name
Date
S
Section
Lessons
Noormal Distrributions
IID
Open
n the interacttive version of the normaal tables or nnormal distriibution appleet (Opens a
separrate browser window)
Obtaiin some picttures of norm
mal curves. Print
P
them ouut and use thhem to help ssolve
probllems.
Exercise
E
I
Part A
p
time X of jazz CDs
C has the normal
n
distriibution with mean 52 annd standard
The playing
deviaation 7; the N(52,
N
7) distrribution.
1. According
g to the 68-9
95-99.7 rule,, what percenntage of jazzz CDs play bbetween 45
and 59 miinutes?
2. What is th
he relative frrequency of jazz
j
CDs wiith playing ttime X less thhan 40
minutes (4
40 minutes is
i a typical playing
p
time for an LP reecord)? Thatt is, find the
relative frrequency of the event X < 40.
3. What is th
he relative frrequency of jazz
j
CDs wiith playing ttime X exacttly 45
minutes?
4. What is th
he relative frrequency of jazz
j
CDs wiith playing ttime over 1 hhour?
Part B
The playing
p
time X of classiccal CDs has the normal ddistribution w
with mean 554 and
stand
dard deviatio
on 5; the N(5
54, 5) distribu
ution.
1. A density
y curve has 3 important features:
f
shappe, center annd spread. C
Compare eachh
of these features
fe
for th
he distributio
ons given inn problems 1 and 2.
2. What is the relative frequency of classical CDs with playing time X less than 40
minutes? That is, find the relative frequency of the event X < 40.
3. What relative frequency of classical CDs have playing time over 1 hour?
4. What is the relative frequency of classical CDs with playing time between 45 and
59 minutes?
Exercise II
SAT (combined) scores of college-bound seniors in high school has the normal
distribution with mean 1050 and standard deviation 150.
1. What is the relative frequency college-bound seniors who have SAT score X less
than 756?
2. Find the value x such that the 0.025 of all seniors have SAT score below x. (Hint:
see part a.). 2.5% of all seniors would have SAT below this value.
3. Find the value x such that the 0.20 of all seniors have SAT score below x.
4. What are the 2.5th and 20th percentiles of this distribution?
5. What is the 97.5th percentile?
6. Use your results to form a 95% probability interval for the SAT score of a
college-bound senior.
Exercise III
A small company records budgeted and actual expenses for each research project it takes
on. For instance, a project is budgeted for $100,000; later the actual cost for the project is
found to be $103,428. This is a difference of $3,428 or 3.428% over budget (projects
finishing under budget are recorded as negatives). You work in accounting where the
percentage over/under-budgeted (the "budget discrepancy") has historically been
modeled with the normal distribution, mean 1.53% and standard deviation 1.06%.
1. There's a variable X here. Describe X.
2. What is the relative frequency of projects that come in under budget?
3. Find the 99th percentile of budget discrepancies. What percentage of budgets
exceed this amount?
4. You examine a year's worth of recent project data: 24 of 498 projects finished
with a budget discrepancy over 4%. Does this information agree with the answer
of part c?