Download STT 315 Practice Problems II for Sections 4.1

STT 315 Practice Problems II for
Sections 4.1 - 4.8
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Classify the following random variable according to whether it is discrete or continuous.
The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
A) continuous
B) discrete
1)
2) Classify the following random variable according to whether it is discrete or continuous.
The number of goals scored in a soccer game
A) discrete
B) continuous
2)
3) Classify the following random variable according to whether it is discrete or continuous.
The number of phone calls to the attendance office of a high school on any given school day
A) continuous
B) discrete
3)
4) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability
distribution is shown below. Find the probability for the value of x = 5.
4)
x
2
3
5
8
10
p(x) 0.10 0.20 ??? 0.30 0.10
A) 0.2
B) 0.3
C) 0.1
D) 0.7
5) The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner
believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies,
and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the
owner bakes 200 pies each day at a cost of $2 each. Assume any pies that go unsold are thrown out
at the end of the day. If she sells the pies for $5 each, find the probability distribution for her daily
profit.
A)
B)
Profit P(profit)
Profit P(profit)
$300
.5
$300
.5
$550
.25
$450
.25
$800
.25
$600
.25
C)
D)
Profit P(profit)
Profit P(profit)
$100
.5
$500
.5
$350
.25
$750
.25
$600
.25
$1000 .25
5)
6) Consider the given discrete probability distribution. Find P(x > 3).
6)
x
p(x)
A) .7
1
.1
2
.2
3
.2
4
.3
5
.2
B) .5
C) .2
1
D) .3
7) Consider the given discrete probability distribution. Find P(x
x
p(x)
0
.30
1
.25
A) .95
2
.20
3
.15
4
.05
B) .05
7)
4).
5
.05
C) .10
D) .90
8) Mamma Temte bakes six pies each day at a cost of $2 each. On 11% of the days she sells only two
pies. On 17% of the days, she sells 4 pies, and on the remaining 72% of the days, she sells all six
pies. If Mama Temte sells her pies for $4 each, what is her expected profit for a day's worth of pies?
[Assume that any leftover pies are given away.]
A) -$8.00
B) -$6.78
C) $20.88
D) $8.88
8)
9) A local bakery has determined a probability distribution for the number of cheesecakes it sells in a
given day. The distribution is as follows:
9)
Number sold in a day
Prob (Number sold)
0
0.06
5
0.2
10
0.13
15
0.08
20
0.53
Find the number of cheesecakes that this local bakery expects to sell in a day.
A) 14.1
B) 10
C) 14.16
D) 20
10) Calculate the mean for the discrete probability distribution shown here.
X
3
4
8
11
P(X) 0.26 0.1 0.06 0.58
A) 6.5
B) 8.04
C) 2.01
10)
D) 26
11) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability
distribution is shown below. Find the standard deviation of the distribution.
11)
x
2
3
5
8
10
p(x) 0.10 0.20 0.30 0.30 0.10
A) 5.7
B) 2.532
C) 6.41
D) 1.845
12) Which binomial probability is represented on the screen below?
A) P(x
4)
B) P(x > 4)
C) P(x < 4)
2
12)
D) P(x = 4)
13) We believe that 95% of the population of all Business Statistics students consider statistics to be an
exciting subject. Suppose we randomly and independently selected 21 students from the
population. If the true percentage is really 95%, find the probability of observing 20 or more
students who consider statistics to be an exciting subject. Round to six decimal places.
A) 0.376410
B) 0.716972
C) 0.340562
D) 0.283028
13)
14) A recent study suggested that 70% of all eligible voters will vote in the next presidential election.
Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a
binomial probability table to find the probability that more than 12 of the eligible voters sampled
will vote in the next presidential election.
A) 0.608
B) 0.887
C) 0.772
D) 0.228
E) 0.392
14)
15) A recent study suggested that 70% of all eligible voters will vote in the next presidential election.
Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a
binomial probability table to find the probability that more than 10 but fewer than 16 of the 20
eligible voters sampled will vote in the next presidential election.
A) 0.649
B) 0.780
C) 0.714
D) 0.845
15)
16) It a recent study of college students indicated that 30% of all college students had at least one tattoo.
A small private college decided to randomly and independently sample 15 of their students and
ask if they have a tattoo. Use a binomial probability table to find the probability that exactly 5 of the
students reported that they did have at least one tattoo.
A) 0.722
B) 0.218
C) 0.207
D) 0.515
16)
17) The probability that an individual is left-handed is 0.13. In a class of 70 students, what is the mean
and standard deviation of the number of left-handed students? Round to the nearest hundredth
when necessary.
A) mean: 70; standard deviation: 3.02
B) mean: 9.1; standard deviation: 3.02
C) mean: 9.1; standard deviation: 2.81
D) mean: 70; standard deviation: 2.81
17)
18) The number of traffic accidents that occur on a particular stretch of road during a month follows a
Poisson distribution with a mean of 8.8. Find the probability that fewer than three accidents will
occur next month on this stretch of road.
A) 0.024434
B) 0.992686
C) 0.975566
D) 0.007314
18)
19) The number of traffic accidents that occur on a particular stretch of road during a month follows a
Poisson distribution with a mean of 8.9. Find the probability of observing exactly four accidents on
this stretch of road next month.
A) 0.035656
B) 174.158539
C) 1.296886
D) 4.788184
19)
20) The university police department must write, on average, five tickets per day to keep department
revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson
distribution with a mean of 8.9. Find the probability that exactly four tickets are written on a
randomly selected day.
A) .964344
B) .058433
C) .941567
D) .035656
20)
21) The number of goals scored at each game by a certain hockey team follows a Poisson distribution
with a mean of 5 goals per game. Find the probability that the team will score more than three
goals during a game.
A) 0.734974
B) 0.124652
C) 0.875348
D) 0.265026
21)
3
22) The number of goals scored at each game by a certain hockey team follows a Poisson distribution
with a mean of 5 goals per game. Find the probability that the team scored exactly three goals in
each of four randomly selected games.
A) 0.00038828
B) 0.56149561
C) 0.43850439
D) 0.00540243
22)
23) An alarm company reports that the number of alarms sent to their monitoring center from
customers owning their system follow a Poisson distribution with = 4.7 alarms per year. Identify
the mean and standard deviation for this distribution.
A) mean = 2.17, standard Deviation = 2.17
B) mean = 4.7, standard Deviation = 2.17
C) mean = 2.17, standard Deviation = 4.7
D) mean = 4.7, standard Deviation = 4.7
23)
24) Given that x is a hypergeometric random variable, compute p(x) for N = 6, n = 3, r = 3, and x = 1.
A) .125
B) .375
C) .45
D) .55
24)
25) Given that x is a hypergeometric random variable, compute p(x) for N = 8, n = 5, r = 3, and x = 2.
A) .536
B) .343
C) .140
D) .464
25)
26) Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All
candidates were told that the positions were randomly filled. Find the probability that two men are
selected to fill the appointed positions.
A) .160
B) .343
C) .360
D) .143
26)
27) Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local
paint store in order to paint his mother's house. Unknown to the man, three of these cans contains
an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these
1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that
are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability
that at least one of the four cans selected contains an incorrect mix of paint.
A) 0.74545
B) 0.49091
C) 0.50909
D) 0.78182
27)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28) You randomly select 7 students from a class with 15 male and 20 female students. What is
the probability that you will choose exactly 4 females?
28)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Answer the question True or False.
29) For a continuous probability distribution, the probability that x is between a and b is the same
regardless of whether or not you include the endpoints, a and b, of the interval.
A) True
B) False
Solve the problem.
30) Use the standard normal distribution to find P(-2.25 < z < 1.25).
A) .8821
B) .8944
C) .4878
31) Use the standard normal distribution to find P(z < -2.33 or z > 2.33).
A) .7888
B) .9809
C) .0606
4
D) .0122
D) .0198
29)
30)
31)
32) Find a value of the standard normal random variable z, called z0 , such that P(-z0
A) 1.96
B) 1.645
C) 2.33
33) Find a value of the standard normal random variable z, called z0 , such that P(z
A) -.47
B) -.53
C) -.81
z
z0 ) = 0.98.
32)
D) .99
z0 ) = 0.70.
33)
D) -.98
34) For a standard normal random variable, find the probability that z exceeds the value -1.65.
A) 0.9505
B) 0.0495
C) 0.5495
D) 0.4505
34)
35) For a standard normal random variable, find the point in the distribution in which 11.9% of the
z-values fall below.
A) 1.18
B) -1.18
C) -0.30
D) -1.45
35)
36) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 450 seconds and a standard deviation of 40 seconds. Find the probability that a randomly
selected boy in secondary school can run the mile in less than 358 seconds.
A) .4893
B) .0107
C) .5107
D) .9893
36)
37) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 470 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize
the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat
in order to earn a certificate of recognition from the fitness association?
A) 371.3 seconds
B) 568.7 seconds
C) 393.2 seconds
D) 546.8 seconds
37)
38) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 440 seconds and a standard deviation of 60 seconds. Between what times do we expect
approximately 95% of the boys to run the mile?
A) between 341.3 and 538.736 seconds
B) between 0 and 538.736 seconds
C) between 322.4 and 557.6 seconds
D) between 345 and 535 seconds
38)
39) The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal
distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce. The company
receives complaints from consumers who actually measure the amount of soda in the cans and
claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans
contain less than the advertised 12 ounces of soda?
A) .4332
B) .5668
C) .0668
D) .9332
39)
40) The weight of corn chips dispensed into a 48-ounce bag by the dispensing machine has been
identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation
of 0.2 ounce. What proportion of the 48-ounce bags contain more than the advertised 48 ounces of
chips?
A) .4938
B) .9938
C) .5062
D) .0062
40)
5
41) The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal
distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce. Each can holds a
maximum of 12.50 ounces of soda. Every can that has more than 12.50 ounces of soda poured into it
causes a spill and the can must go through a special cleaning process before it can be sold. What is
the probability that a randomly selected can will need to go through this process?
A) .3413
B) .6587
C) .8413
D) .1587
41)
42) Before a new phone system was installed, the amount a company spent on personal calls followed
a normal distribution with an average of $900 per month and a standard deviation of $50 per
month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what
is the probability that during a randomly selected month PCE's were between $775.00 and $990.00?
A) .0001
B) .9579
C) .0421
D) .9999
42)
43) Which of the following statements is not a property of the normal curve?
A) P(µ - < x < µ + ) .95
B) mound-shaped (or bell shaped)
C) symmetric about µ
D) P(µ - 3 < x < µ + 3 ) .997
43)
44) Which one of the following suggests that the data set is not approximately normal?
A)
44)
B) A data set with 68% of the measurements within x ± 2s.
C) A data set with IQR = 752 and s = 574.
D)
Stem
Leaves
3
0 3 9
4
2 4 7 7
5
1 3 4 8 8 9 9 9
6
0 0 5 6 6 7 8
7
1 1 5
8
2 7
6
45) Data has been collected and a normal probability plot for one of the variables is shown below.
Based on your knowledge of normal probability plots, do you believe the variable in question is
normally distributed? The data are represented by the"o" symbols in the plot.
45)
A) No. The plot does not reveal a straight line and this indicates the variable is not normally
distributed.
B) Yes. The plot reveals a curve and this indicates the variable is normally distributed.
C) Yes. The plot reveals a straight line and this indicates the variable is normally distributed.
Find the probability.
46) Suppose x is a random variable best described by a uniform probability distribution with c = 30
and d = 90. Find P(30 x 60).
A) 0.5
B) 0.6
C) 0.3
D) 0.05
46)
47) Suppose x is a random variable best described by a uniform probability distribution with c = 20
and d = 40. Find P(x < 30).
A) 0.6
B) 0.5
C) 0.05
D) 0.1
47)
48) Suppose x is a random variable best described by a uniform probability distribution with c = 10
and d = 70. Find P(x > 55).
A) 0.15
B) 0.025
C) 0.75
D) 0.25
48)
Solve the problem.
49) A machine is set to pump cleanser into a process at the rate of 7 gallons per minute. Upon
inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform
distribution over the interval 6.5 to 9.5 gallons per minute. Find the probability that between 7.0
gallons and 8.0 gallons are pumped during a randomly selected minute.
A) 0
B) 1
C) 0.33
D) 0.67
7
49)
50) The diameters of ball bearings produced in a manufacturing process can be described using a
uniform distribution over the interval 2.5 to 4.5 millimeters. What is the mean diameter of ball
bearings produced in this manufacturing process?
A) 3.5 millimeters
B) 3.0 millimeters
C) 4.5 millimeters
D) 4.0 millimeters
50)
51) Suppose x is a uniform random variable with c = 20 and d = 90. Find the standard deviation of x.
A) = 31.75
B) = 3.03
C) = 20.21
D) = 2.42
51)
52) The diameters of ball bearings produced in a manufacturing process can be described using a
uniform distribution over the interval 8.5 to 10.5 millimeters. Any ball bearing with a diameter of
over 10.25 millimeters or under 8.75 millimeters is considered defective. What is the probability
that a randomly selected ball bearing is defective?
A) 0
B) .25
C) .75
D) .50
52)
53) A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon
inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform
distribution over the interval 9.5 to 12.5 gallons per minute. What is the probability that at the time
the machine is checked it is pumping more than 11.0 gallons per minute?
A) .667
B) .7692
C) .25
D) .50
53)
54) A machine is set to pump cleanser into a process at the rate of 6 gallons per minute. Upon
inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform
distribution over the interval 5.5 to 9.5 gallons per minute. Find the variance of the distribution.
A) 1.33
B) 18.75
C) 3.00
D) 0.75
54)
55) The time between customer arrivals at a furniture store has an approximate exponential
distribution with mean = 8.5 minutes. If a customer just arrived, find the probability that the next
customer will arrive in the next 5 minutes.
A) 0.555306
B) 0.444694
C) 0.817316
D) 0.182684
55)
56) The time between customer arrivals at a furniture store has an approximate exponential
distribution with mean = 8.5 minutes. If a customer just arrived, find the probability that the next
customer will not arrive for at least 20 minutes.
A) 0.653770
B) 0.095089
C) 0.904911
D) 0.346230
56)
57) The time (in years) until the first critical-part failure for a certain car is exponentially distributed
with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5
years or more.
A) 0.770210
B) 0.506617
C) 0.493383
D) 0.229790
57)
58) The time (in years) until the first critical-part failure for a certain car is exponentially distributed
with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is less
than 1 year.
A) 0.033373
B) 0.745189
C) 0.254811
D) 0.966627
58)
59) The time between arrivals at an ATM machine follows an exponential distribution with = 10
minutes. Find the probability that between 15 and 25 minutes will pass between arrivals.
A) 0.141045
B) 0.082085
C) 0.305215
D) 0.223130
59)
8
Answer the question True or False.
60) The probability density function for an exponential random variable x has a graph called a bell
curve.
A) True
B) False
61) The exponential distribution has the property that its mean equals its standard deviation.
A) True
B) False
Solve the problem.
62) Suppose that the random variable x has an exponential distribution with
probability that x will assume a value within the interval µ ± 2 .
A) .864665
B) .049787
C) .716531
= 1.5. Find the
61)
62)
D) .950213
63) The time between arrivals at an ATM machine follows an exponential distribution with = 10
minutes. Find the mean and standard deviation of this distribution.
A) Mean = 10, Standard Deviation = 3.16
B) Mean = 3.16, Standard Deviation = 3.16
C) Mean = 10, Standard Deviation = 100
D) Mean = 10, Standard Deviation = 10
9
60)
63)
Answer Key
Testname: PRACTICE2 4.1-4.8
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A
A
B
B
C
B
A
D
A
B
B
A
B
C
C
C
C
D
A
D
A
A
B
C
A
B
A
28) P(x = 0) =
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20 15
4 3
35
7
.328
A
A
D
C
B
A
B
B
C
C
C
B
D
B
A
B
A
A
10
B
D
C
A
C
B
D
A
B
B
D
C
A
B
A
D
D