Download Ch 2 Test Remediation Work - Anoka

Ch 2 Test Remediation Work
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) High temperatures in a certain city for the month of August follow a uniform distribution over the
interval 60°F to 85°F. What is the probability that a randomly selected August day has a high
temperature that exceeded 65°F?
A) 0.04
B) 0.8
C) 0.4483
D) 0.2
1)
2) High temperatures in a certain city for the month of August follow a uniform distribution over the
interval 73°F to 103°F. Find the high temperature which 90% of the August days exceed.
A) 100°F
B) 103°F
C) 83°F
D) 76°F
2)
3) 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. Find the probability that between 10.0
gallons and 11.0 gallons are pumped during a randomly selected minute.
A) 0.33
B) 0.67
C) 1
D) 0
3)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4) You are performing a study about the weight of preschoolers. A previous study found the
weights to be normally distributed with a mean of 30 and a standard deviation of 4. You
randomly sample 30 preschool children and find their weights to be as follows.
25 25 26 26.5 27
27 27.5 28 28
28.5
29 29 30 30
30.5 31 31
32 32.5 32.5
33 33 34 34.5 35
35 37
37 38
38
a) Draw a histogram to display the data. Is it reasonable to assume that the weights are
normally
distributed? Why?
b) Find the mean and standard deviation of your sample.
c) Is there a high probability that the mean and standard deviation of your sample are
consistent
with those found in previous studies? Explain your reasoning.
1
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
5) The graph of a normal curve is given. Use the graph to identify the value of µ and .
753
785
817
A) µ = 32, = 849
849
881
913
B) µ = 96, = 849
945
C) µ = 849,
= 32
D) µ = 849,
5)
= 96
6) The normal density curve is symmetric about
A) Its mean
B) A point located one standard deviation from the mean
C) An inflection point
D) The horizontal axis
6)
7) The area under a standard normal density curve with mean of 0 and standard deviation of 1 is
A) 1
B) µ + 2(3 )
C) µ + 3
D) infinite
7)
8) The highest point on the graph of the normal density curve is located at
A) µ +
B) its mean
C) an inflection point
D) µ + 3
8)
9) Approximately ____% of the area under the normal curve is between µ A) 95
B) 68
C) 99.7
and µ + .
D) 50
9)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
10) The weight of 2-year old hyraxes is known to be normally distributed with mean
µ = 2200 grams and standard deviation = 365 grams
(a) Draw a normal curve with the parameters labeled.
(b) Shade the region that represents the proportion of hyraxes who weighed more than
2930 grams.
(c) Suppose the area under the normal curve to the left of X = 2930 is 0.0228. Provide two
interpretations of this result.
10)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
11) Find the area under the standard normal curve between z = 0 and z = 3.
A) 0.0010
B) 0.9987
C) 0.4641
D) 0.4987
12) Find the area under the standard normal curve between z = 1 and z = 2.
A) 0.5398
B) 0.8413
C) 0.1359
D) 0.2139
2
11)
12)
13) Find the area under the standard normal curve between z = -1.25 and z = 1.25.
A) 0.6412
B) 0.8817
C) 0.2112
D) 0.7888
13)
14) For a standard normal curve, find the z-score that separates the bottom 30% from the top 70%.
A) -0.47
B) -0.53
C) -0.98
D) -0.12
14)
15) Find the z-score that is less than the mean and for which 70% of the distribution's area lies to its
right.
A) -0.47
B) -0.98
C) -0.81
D) -0.53
15)
16) For a standard normal curve, find the z-score that separates the bottom 90% from the top 10%.
A) 1.28
B) 2.81
C) 1.52
D) 0.28
16)
17) Scores on a standardized test are normally distributed with a mean of 96 and a standard deviation
of 12. An individual's test score is found to be 128. Find the z-score corresponding to this value.
A) -0.37
B) 0.38
C) -2.67
D) 2.67
17)
18) Use the standard normal distribution to find P(-2.25 < Z < 0).
A) 0.0122
B) 0.4878
C) 0.6831
18)
19) Use the standard normal distribution to find P(Z < -2.33 or Z > 2.33).
A) 0.7888
B) 0.0198
C) 0.9809
D) 0.5122
D) 0.0606
19)
Determine the area under the standard normal curve that lies a) above and b) below the given z-score.
20) z = -0.2
A) 0.4207, 0.4207
B) 0.5793, 0.5793
C) 0.5793, 0.4207
D) 0.4207, 0.5793
20)
Determine the area under the standard normal curve that lies between:
21) z = 0.9 and z = 1.4
A) 0.1033
B) 0.9192
C) 0.1841
21)
22) z = -2 and z = -0.2
A) 0.0228
B) 0.5793
C) 0.4207
D) 0.8159
D) 0.3979
Provide an appropriate response.
23) 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 50 seconds. Find the probability that a randomly
selected boy in secondary school will take longer than 355 seconds to run the mile.
A) 0.4893
B) 0.0107
C) 0.9893
D) 0.5107
24) 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. Find the probability that a randomly
selected boy in secondary school can run the mile in less than 302 seconds.
A) 0.4893
B) 0.5107
C) 0.9893
D) 0.0107
3
22)
23)
24)
25) The tread life of a particular brand of tire is a random variable best described by a normal
distribution with a mean of 60,000 miles and a standard deviation of 1400 miles. What is the
probability a certain tire of this brand will last between 57,060 miles and 57,480 miles?
A) 0.4920
B) 0.0180
C) 0.4649
D) 0.9813
25)
26) 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 most
(approximately 95%) of the boys to run the mile?
A) between 345 and 535 sec
B) between 341.3 and 538.736 sec
C) between 0 and 538.736 sec
D) between 322.4 and 557.6 sec
26)
27) The length of time it takes college students to find a parking spot in the library parking lot follows a
normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the
cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the
library parking lot.
A) 5.3 min
B) 5.0 min
C) 5.2 min
D) 4.8 min
27)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28) The board of examiners that administers the real estate broker's examination in a certain
state found that the mean score on the test was 504 and the standard deviation was 72. If
the board wants to set the passing score so that only the best 80% of all applicants pass,
what is the passing score? Assume that the scores are normally distributed.
28)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
29) 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 50 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) 386 sec
B) 367.75 sec
C) 532.25 sec
D) 514 sec
4
29)
Answer Key
Testname: CH 2 TEST REMEDIATION WORK
1)
2)
3)
4)
B
D
A
(a)
It is not reasonable to assume that the heights are normally distributed since the histogram is skewed.
(b) µ = 31,
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
= 3.86
(c) Yes. The mean and standard deviation are close.
C
A
A
B
B
(a), (b)
(c) The two interpretations are: (1) the proportion of hyraxes who weighed more than 2930 is 0.0228 and (2) the
probability that a randomly selected hyrax weighs more than 2930 is 0.0228.
D
C
D
B
D
5
Answer Key
Testname: CH 2 TEST REMEDIATION WORK
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
A
D
B
B
C
A
D
C
D
B
D
C
Let x be a score on this exam. Then x is a normally distributed random variable with µ = 504 and
find the value of x0, such that P(x > x0 ) = 0.80. The z-score for the value x = x0 is
z=
x0 - µ
=
x0 - 504
72
P(x > x0) = P z >
We find
x2 - 504
x0 - 504
72
x0 - 504 = -0.84(72)
29) A
.
72
= 0.80
-0.84.
x0 = 504 - 0.84(72) = 443.52
6
= 72. We want to