Transcript Review for 2nd nine weeks testx

nd
2
Review for
Weeks Test
Nine
1) The distribution of SAT Math scores of students taking
Calculus I at UTSA is skewed left with a mean of 625 and a standard deviation of
44.5. If random samples of 100 students are repeatedly taken, which statement
best describes the sampling distribution of sample means?
A) Shape is normal with a mean of 625 and standard deviation of 44.5.
B) Shape is normal with a mean of 625 and standard deviation of 4.45.
C) Shape unknown with a mean of 625 and standard deviation of 44.5.
D) Shape unknown with a mean of 625 and standard deviation of 4.45.
E) No conclusion can be drawn since the population is not normally distributed.
Answer
• Formula:
•
• Or
•
𝜎2
𝑛
44.52
100
𝜎
simply:
𝑛
44.5
100
These answers are the
same
2) A population has a normal distribution with a mean
of 50 and a standard deviation of 10. If a random
sample of size 9 is taken from the population, then
what is the probability that this sample mean will be
between 48 and 54?
A)0.000
D) 0.399
B) 0.228
E) 0.611
C) 0.385
Answer
• P(48<𝑥<54)=
48−50
10
9
<Z<
54−50
10
9
• P(-.6<𝑥<1.2) = (Z score for -.6) + (Z score for -1.2) = .2257 + .3849 =
.6106
3) Owners of a day-care chain wish to determine the proportion of
families in need of day care for the town of Helotes. The owners of
the day-care chain randomly sample 50 Helotes families and find only
4% of the returned questionnaires indicate these families having a
need for child day-care services. The 4% is best described as
A) the sample proportion of families in Helotes needing child day-care
services.
B) the sample proportion of families in Helotes with children needing
day-care services.
C) the population proportion of families in Helotes with children needing
day-care services.
D) the 30 families in Helotes needing day-care services for their
children.
E) the 600 families in Helotes with children needing day-care services.
Answer
• Since the survey was to indicate the families having a need for child
day-care services, that is what the 4% represents.
A coach in a large high school thinks that ballet training will
improve the batting performance of his baseball team. He
decides to have a randomly selected half of the team take
six weeks of ballet training before the baseball season
begins while the other half does not take such training. He
will then compare the season batting averages of group A
(those with ballet training) and group B (those without ballet
training) by comparing the mean of group A with the mean
of group B.
4) This study would be classified as:
a. a survey
b. an observational study
c. an experimental study
Answer
• Study has a treatment, so it can not be observational. It obviously is
not a survey.
A coach in a large high school thinks that ballet training will
improve the batting performance of his baseball team. He
decides to have a randomly selected half of the team take
six weeks of ballet training before the baseball season
begins while the other half does not take such training. He
will then compare the season batting averages of group A
(those with ballet training) and group B (those without ballet
training) by comparing the mean of group A with the mean
of group B.
5) The response variable is:
a. ballet training
b. batting average
c. runs batted in
d. the size of the school
e. the grades the players make in the ballet school
Answer
• Response variable is like a dependent variable...batting average is
dependent.
6)If P(A) = 0.24 and P(B) = 0.52 and events A and
B are independent, what is P(A or B)?
a)0.1248
c) 0.6352
b) 0.2800
d) 0.7600
e) The answer cannot be determined from the
information given.
Answer
• P(A or B) = P(A) + P(B) - P(A and B)
• As A and B are independent
• P(A and B) = P(A)P(B).
So, P(A or B) = .24 + .52 - .24x.52 = .6252
7) Before premiering a blockbuster movie at a theater, test
screenings are done beforehand. A small number of selected
theaters are chosen geographically throughout the country. Each
theater chosen is supposed to be representative of theatergoers in
that area. Everyone is interviewed when the movie is over.
Identify the type of sampling used in this example.
A)Stratified sampling
B) SRS
C) Cluster Sampling
D) Systematic Sampling
E) Convenience Sampling
Answer
• Since a small number of theatres are chosen in a location
geographically and then a census is done to that sample this is cluster
sampling.
8) A test consists of 10 true/false questions. If a student
guesses on each question, what is the probability that
the student will answer at least 9 questions correctly?
A)0.9
B) 0.001
D) 0.999
E) 0.011
C) 0.010
Answer
• This is a problem on binomial probabilities. The probability of success (correct answer) p is 0.5; respectively
the probability of failure is also 0.5.
• The number of experiments n is 10. We are interested in probability that the number of successes is at least
9
• P(X≥9) = P(X=9) + P(X=10)
•
10𝐶 9
=
1
( 2)9 ∙
1−
1 10−9 1 10
+( 2) ∙
2
1−
1 10−10
2
= 0.001953
• At least 9 would be 9, or 10 so you'd have to do each then add the answers.
Formula is nCr p^r q^ (n - r) where
n = total possible
r = number of successes
p = probability of success
q = prob. of failure
6: 10C9 (1/2)^9 (1-1/2)^1 = 1/1024
7: 10C10 (1/2)^10 (1-1/2)^0 = 1/1024
9) A basketball player has made 66% of his foul shots
during the season. Assuming the shots are independent,
find the probability that in tonight's game he misses for
the first time on his 6th attempt?
A) 0.0426
B) 0.0281
D) 0.0827
E) 0.34
C) 0.1252
Answer
• Geometric
• P(miss, q) = .34, P(makes, p) = .66,
• P(x = 1) = geometpdf(.34, 6) or simply
• (.66)^5(.34)
At George Washington High School students are heavily involved in extracurricular activities. Suppose that a student is selected at random from the
students at this school. Let the events A, M, and S be defined as follows, with
probabilities listed:
A = student is active in the performing arts:
P(A) = 0.20
M = student is active in vocal or instrumental music: P(M) = 0.32
S = student is active in sports:
P(S) = 0.35
∩ S ) = 0.07; P( M | S ) = 0.30
∩ M ) = 0.18; P( A Ç
P( A Ç
Calculate the following (show your work):
P( M  S )
P( M | S ) 
P( S )
P( M  S )
0.30 
0.35
0.105  P( M  S )
P( M ∩
Ç S)
2ND Nine weeks Review – Ch 11-18
1)B
2) E
3) A
4) C
5) B
6) C
7) C
8) E
9) A