Review #2 Ch. 6-8
AP STATS
Name________________
Date________Per______
CH. 6 MULTIPLE CHOICE
1.
The conditional probability that the event E
occurs given the event F has occurred is
P( E  F )
P( E )
P( E  F )
b.
P( E )
P( E  F )
c.
P( F )
P( E  F )
d.
P( F )
2.
If P(A) =.5,P(B) =.3 and P( A  B) = .15,then
a. A and B are disjointed events.
b. A and B are mutually exclusive events.
c. A and B are dependent events.
d. A and B are independent events.
3.
Which of the following is not a probability
rule?
a. P(A) = 1- P( A c )
b. P( A  B)  P( A)  P( B).
c. P( A  B)  P( A)  P( B)  P( A  B).
a.
d. P( A  B)  P( A) P( B A).
4.
If a fair coin is flipped twice with the outcome of each flip independent of each other, then the
probability that at least one of the two flips results in a head is
a. ¼
c. ¾
b. ½
d. 1
5.
Only twenty percent of the applicants for new positions at a large software company are female.
Assuming that two positions will be filled independently of each other, what is the probability that
both positions are filled by females?
a. .36
c. .96
b. .64
d. .04
6.
Two event A and B are said to be independent when
a. P( A)  1  P( B)
c. P( A B)  P( A)
b. P( A B)  P( B)
d. P( A  B)  P( A)  P( B)
7.
A family is going shopping for a new van. The probability that the family will purchase a Ford van
is .33, a Chevy van .25, a Doge van .20, and Toyota van .22. The probability that the family
purchases a Toyota van or a Ford van or a Chevy van is:
a. .33  .22  .25
c. 1- .33  .22  .25
b. .33+ .22+ .25
d. 1- (.33+.22+.25)
8.
Suppose there are 60 students in a statistics class of which 24 are female. If three students are selected
without replacement to work problems at the board, what is the probability that all 3 of the students chosen
are female?
a. 24/60+23/59+22/58
c. 24/60  23/59  22/58
b. 24/60+23/60+22/60
d. 24/60  23/59  22/58
9.
The probability that a new tire will have a blowout in the first year is .10. If the four tires on a new car
function independently of each other, what is the probability that at least one tire blows out in
the first
year?
a. .10  .10  .10  .10
c. .90  .90  .90  .90
b. 1-(.10  .10  .10  .10)
d. 1-(.90  .90  .90  .90)
10.
For a random sample of size n taken from a population of size N, independence can be assumed
for purposes of calculation of probabilities when
a. n is no larger than 5% of N
c. n is no larger than 50% of N
b. n is at least 5% of N
d. n is at least 50% of N
CH. 6 SHORT ANSWER:
11.
Explain what it means for two events to be independent.
12.
Under what conditions is the probability that event A or event B occurs equal to the sum of their
probabilities?
13.
Under what conditions is the probability that both events A and B occur equal to the product of their
probabilities?
14.
A paranormal researcher is studying ESP and has developed a test consisting of 5 independent items. She
has simulated the probabilities of getting 0, 1, 2, 3, 4, or 5 of the test items correct by guessing and has
constructed the following distribution.
# Correct 0 1
2
3
4
5
Frequency 28 151 308 317 163 33
a. Estimate the probabilities of getting 0, 1, 2, 3, 4, or 5 correct when a person taking the test guesses on
each item.
b. Estimate the probability that a person taking the test by guessing at each item gets at least 3 correct.
c. Using the estimated probabilities, do you believe that a person who gets all 5 items correct is guessing?
Explain.
15.
A large manufacturing company runs day and night work shifts in producing their product. The day shift
produces 60% of the product and the night shift 40% of the product. Furthermore, 5% of the product is
defective given that it was produced during the day shift and 2% is defective given that it was produced
during the night shift.
Tree
Diagram:
a. Determine the probability that a defective product is produced by this company.
b. Determine the probability that the day shift produced the product given that it is defective.
c. Determine the probability that the night shift produced the product given that it is defective.
16.
Two different alloys are used in making car wheels at the Fjord Motor Company with 30% of the cars
having wheels make of alloy I and 70% having alloy II. Supposed that the probability that a crack develops
in a wheel is .1 given the wheel is made of alloy I and .05 given alloy II.
Tree
Diagram:
a. Determine the probability that a Fjord car wheel develops a crack.
b. Given that a wheel has a crack, what is the probability that it was made from alloy I?
c. Given that a wheel has a crack, what is the probability that it was made from alloy II?
Suppose P(A)= .65, P(B) = .60 and P( A  B) = .45 Determine
17.
a. P( Ac ) =______
b. P( A  B) =_______
18.
c. P( A B) =_______
d. whether A and B are independent events.______
Canada has developed a new missile that hits its target 60% of the time. I f two missiles are fired
independently of each other at a target, what is the probability that
a. both missiles hit the target?
b. at least one missile hits the target?
19.
Suppose P(A)=.15, P(B) = .4 and P(C)= .2 Determine
a. P( A  B  C ) when A, B, C are mutually exclusive.
b. P( A  B  C ) when, A, B, C are mutually independent.
CH. 7 MULTIPLE CHOICE
20.
For a standard normal variable, z, P( z  -2.08) =
a. .0188
c. .9812
b. .0026
d. .9974
21.
For a normal variable x having mean 100 and standard deviation 5, the largest 10% of the population
values exceed
a. –1.28
c. 93.6
b. 1.28
d. 106.4
22.
Which of the following statements is not true about a normal curve?
a. Every normal curve is symmetric.
b. Every normal curve is symmetric about 0.
c. Every normal curve is bell-shaped.
d. Every normal curve is centered at its mean.
23.
The proportion that a normal variable x falling within 2 standard deviations of the mean is
a. .0228
c. .0456
b. .9772
d. .9544
24.
Which of the following is not a property of a binomial experiment?
a. It consists of a fixed number of trials n.
b. Outcomes of a different trials are independent.
c. Each trial can result in one of several different outcomes.
d. x = the number of successes observed when the experiment is performed.
25.
If x is a binomial random variable with n =10 and p = .25, then
a.  x  1.875
c.  x  1.875
b.  x  2.5
d.  x  1.875
2
26.
Which of the following is not a property of a geometric experiment?
a. It consists of a fixed number of trials n.
b. Outcomes of different trials are independent.
c. Each trial can result in one of two possible outcomes.
d. The probability of success is the same for all trials.
27.
If x is a binomial random variable with n = 10 and p= .4, then the binomial probability function can be
written as
.4
.6
x
10 x
a. p ( x)  (10
c. p( x)  (10
.4 )  x (1  x )
x )  .6 (.4)
x
10 x
b. p( x)  (10
. x )  .4 (.6)
x
)  .4 x (.6)10 x
d. p( x)  (10
CH. 7 SHORT ANSWER:
28.
What is the difference between a discrete random variable and a continuous variable?
29.
What is the difference between a standard normal distribution and a general normal distribution?
30.
What are the 4 conditions of a binomial experiment?
31.
What are the 3 conditions of a geometric experiment?
32.
A fair die will be rolled until a six appears. Let x= the number of rolls be required in order to roll a six.
a. Determine the probability that x=2.
b. Determine the probability that x  4.
33.
Let x= The distance put on a particular model of Goodrich tire before it needs replacement. Suppose
that a normal distribution with the mean 40,000 miles and standard deviation 4,000 miles is a
reasonable model for describing the population distribution of x.
a. What is the probability that a randomly selected Goodrich tire of this model lasts between 30,000
and 50,000 miles?
b. What is the probability that a randomly selected Goodrich tire of this model lasts at least 53,000
miles?
c. What is the value of x that is exceeded by only the largest 5% of the population values?
d. If two of this particular model of Goodrich tire are selected at random and independently of each
other, what is he probability that they both last at least 53,000 miles?
34.
Let x= the diameter of the pupil if a human eye under normal ambient light. Suppose that the variable x
had a distribution that is well approximated by a normal distribution with mean .6 cm and standard
deviation .05 cm.
a. What is the probability that a randomly selected human eye has a pupil diameter no more than .5
cm under normal ambient light?
b. What is the probability that a randomly selected human eye has a pupil having a diameter between
.55 and .75 cm under normal ambient light?
c. What is the value of x that is exceeded by only the largest 10% of the population values?
35.
Let x= the length of an award winning documentary. Suppose that the variable x has a distribution that
is well approximated by a normal distribution the mean 50 minutes and standard deviation 5 minutes.
a. What is the probability that a randomly selected award-winning documentary is longer than 66
minutes?
b. What is the probability that a randomly selected award winning documentary is between 36 and 60
minutes long?
c. What is the value of x that is exceeded by only the largest 15% of the population values?
d. If a documentary longer than 65 minutes will not be considered for a particular award, what
percentage of award winning documentaries would this exclude from consideration?
CH 8 MULTIPLE CHOICE
37. Which of the following is not a statistic?
a. p̂
b. x
d.  x
c. s
38. Which of the following statements is not true concerning the distribution of x ?
a.
 x , no matter how large n is.
b.  x 

n
c. The distribution of x is normal, no matter how large n is.
d. The distribution of x is normal, no matter how large n is, when the population being sampled
follows a normal distribution.
39. If p = .95, then the smallest value of n for which the distribution of p̂ will be reasonably approximated by
a normal distribution is
a. n = 10
b. n = 30
c. n = 50
d. n = 200
40. The Central Limit Theorem predicts that
a. The sampling distribution of  x will be approximately normal for reasonably large samples.
b. The sampling distribution of x will be approximately normal for reasonably large samples.
c. The mean of the sampling distribution of x will tend to be close to  for reasonably large
samples.
d. The mean of the sampling distribution of  x will tend to be close to  for reasonably large
samples.
41. The Central Limit Theorem predicts that
a. the sampling distribution of p will be approximately normal when np  10 .
b. the sampling distribution of p will be approximately normal when n(1  p)  10 .
c. the sampling distribution of p will be approximately normal when n>30.
d. the sampling distribution of p will be approximately normal when np  10 and n(1  p )  10 .
42. Which of the following statements concerning the Central Limit Theorem is true?
a. The Central Limit Theorem predicts that the distribution of x follows a normal distribution for
every sample size n
b. The Central Limit Theorem predicts that the distribution of p̂ follows a normal distribution for
every sample size n
c. The Central Limit Theorem predicts that the distribution of p̂ will be reasonably close to a normal
distribution when n > 30
d. The Central Limit Theorem predicts that the distribution of x will be reasonably close to a normal
distribution when n > 30
43. Determine in which of the following scenarios the distribution of p̂ will tend to be closest to p.
a. n = 25 and p = .2
c. n = 150 and p = .3
b. n = 25 and p = .9
d. n = 50 and p = .7
CH. 8 SHORT ANSWER:
44. A random sample is to be selected from a population with mean u = 50 and  = 10.
a. Determine the mean and the standard deviation of the sampling distribution of x
when n = 25.
b. How large would n need to be for  x to be less than .5?
c. In general, what happens to the standard deviation of x when four times as many observations are
sampled?
d. Determine the approximate probability that x will be less than 49 when n =100.
45. A pharmacist finds that 55% (p = .55) of all the customers prefer name brand prescription drugs to generic
prescription drugs. For a sample of n = 25 customers, let p̂ = the sample proportion of customers who
prefer name brand prescription drugs.
a. Determine the mean and the standard deviation of the sampling distribution of p̂ .
b. Is it reasonable to assume that the sampling distribution of p̂ is approximately normally
distributed?
c. What is the approximate probability that the sample proportion p̂ is between .50 and .70?
d. Approximately 95% of the time, p̂ is within
of p.
MORE CH. 7 SHORT ANSWER:
46. The number of gad pumps in use at any time during the rush at a local filling station has the following
population distribution.
X
0
1
2
3
4
5
6
7
8
P(x)
.05
.10
.10
.15
.20
.15
.10
.10
.05
a. Determine the probability that at least 5 gas pumps are in use at any time during rush hour.
b. Determine the probability that at least 3 gas pumps and no more than 5 are used at any given time
during rush hour.
c. What is the mean number of gas pumps to be in use?
d. What is the standard deviation of x?
e. If a caravan of 4 cars is going to stop and fill up during rush hour, what is the probability that
enough gas pumps will be open when they arrive at the station?
47. Suppose the probability that an environmental engineer successfully lands a consulting job is 0.30 on each
job bid on. Assume that the consulting jobs bid on are independent, and let x be the number of jobs landed
in 5 jobs bid.
a. What is the probability of landing exactly 3 consulting jobs?
b. Find the probability of landing at most 2 jobs.
c. Find the probability of landing at least 4 jobs.
d. Determine the mean and standard deviation of x.
48. Suppose the probability that a computer part is defective is 0.10. Let x be the number of defective
computer parts in a shipment of 10 parts.
a. What is the probability that there are exactly 5 defective parts in a shipment?
b. Find the probability that there is more than 1 defective parts in a shipment.
c. What is the mean number of defectives in a shipment of 10 parts?
d. What is the standard deviation of the number of defectives in a shipment of 10 parts?
Answers:
Ch. 6:
1) D 2) D 3) B 4) C 5) D 6) C 7) B 8) C 9) D 10) A
11) Two events are independent if the knowledge of event A does not change the outcome of event B
12) When the two events cannot occur simultaneously. 13) When the two events are independent.
14) a. .028, .151, .308, .317, .163, .033 b. .513, c. no, it is unlikely to get all 5 correct by guessing.
15) a. .038 b. .789 c. .211 16) a. .065 b. .462 c. .538
17) a. .35 b. .8 c. .75 d. no (.75)  .6 18) a. .36 b. .84 19) a. .75 b. .012
Ch. 7:
20) A 21) D 22) B 23) D 24) C 25) C 26) A 27) B 28) Discrete=things that are counted, Continuous=things that are
measured 29) Standard normal has a mean of 0, s=1, general normal can have any mean or s. 30) 1. Fixed # of
trials, 2. S or F 3. Ind 4. Same Prob for each trial 31) 1. Same as Binomial, but no Fixed # trials 32) a. .139 b. .5177
33) a. .9876 b. .0006 c. 46580 d. .00000036 34) a. .0028 b. .84 c. .664 35) a. .007 b. .9747 c. 55.2 d. .0013
Ch. 8:
37) D 38) C 39) D 40) B 41) D 42) D 43) C 44) a. 50, 2 b. at least 400 c. cut in half d. .1587
45) a. .55, .0995 b. yes, np  10 c. .6260 d. .199
More Ch. 7:
46) a. .4 b. .5 c. 4 d. 2.12 e. .6 47) a. .1323 b. .8369 c. .0308 d. 1.5, 1.025 48) a. .0015 b. .2639 c. 1 d. .95