Download 2015 Spring Test 3c

Stat 210
Exam Three
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Read these directions carefully. You may pick one problem to omit by writing ʺomitʺ in the answer space. If you do not,
or omit more than one, all problems will be graded. Relax and use your time wisely.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Construct a normal quartile plot of the given data. Use your plot to determine whether the data come from a normally
distributed population. Explain your answer.
1) The weekly incomes (in dollars) of a sample of 12 nurses working at a Los Angeles
hospital are given below.
500 750 630 480
550 650 720 780
820 820 850 770
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
2) Which of the following is not a biased statistic?
A) variance
C) range
2)
B) standard deviation
D) median
Identify the given random variable as being discrete or continuous.
3) The exact braking time of a car
A) Discrete
B) Continuous
3)
Using the following uniform density curve, answer the question.
4) What is the probability that the random variable has a value less than 6.4?
A) 0.5500
B) 0.8000
C) 0.6750
4)
D) 0.9250
Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread
evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of
pounds lost.
5)
5) Between 10.5 pounds and 12 pounds
1
1
3
1
B)
C)
D)
A)
3
2
4
4
If z is a standard normal variable, find the probability.
6) The probability that z lies between -1.10 and -0.36
A) 0.2237
B) -0.2237
6)
C) 0.2239
1
D) 0.4951
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
7) Shaded area is 0.4013.
7)
z
A) -0.25
C) -0.57
B) 0.25
D) 0.57
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
8)
8)
-2.34
-1.17
2.34 z
1.17
A) 0.7580
B) 0.8790
C) 0.1210
D) 0.2420
9)
9)
-3.39 -2.26 -1.13
A) 0.1292
1.13
2.26
3.39
z
B) 0.8485
C) 0.8708
D) 0.8907
10) If 9% of the thermometers are rejected because they have readings that are too low, but all other
thermometers are acceptable, find the temperature that separates the rejected thermometers from
the others.
A) -1.26°
B) -1.34°
C) -1.39°
D) -1.45°
Find the indicated value.
11) z 0.05
A) 1.545
10)
11)
B) 1.645
C) 1.755
2
D) 1.325
Provide an appropriate response.
12) Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are
normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
A) 0.7745
B) 0.7303
C) 0.7619
D) 0.7938
13) Which of the following is true about the distribution of IQ scores?
A) The median is 10.
B) The standard deviation is 10.
C) The mode is 200.
D) The mode is 100.
Find the indicated probability.
14) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard
deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g.
What percentage of legal quarters will be rejected?
A) 1.62%
B) 2.48%
C) 0.0196%
D) 1.96%
Assume that X has a normal distribution, and find the indicated probability.
15) The mean is μ = 15.2 and the standard deviation is σ = 0.9.
Find the probability that X is greater than 17.
A) 0.9772
B) 0.9821
C) 0.9713
Find the indicated critical z value.
18) Find the critical value z α/2 that corresponds to a 90% confidence level.
C) 1.75
3
14)
D) 0.0228
17) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.
A) 0.9146
B) 0.7285
C) 0.8457
D) 0.8531
B) 2.33
13)
15)
Solve the problem.
16) The scores on a certain test are normally distributed with a mean score of 45 and a standard
deviation of 4. What is the probability that a sample of 90 students will have a mean score of at
least 45.4216 ?
A) 0.3174
B) 0.8413
C) 0.3413
D) 0.1587
A) 1.28
12)
16)
17)
18)
D) 1.645
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
19) n = 70, x = 24; 95% confidence
19)
A) 0.250 < p < 0.436
B) 0.249 < p < 0.437
C) 0.232 < p < 0.454
D) 0.249 < p < 0.250
Use the given data to find the minimum sample size required to estimate the population proportion.
^
20) Margin of error: 0.05; confidence level: 99%; from a prior study, p is estimated by 0.07.
A) 208
B) 100
C) 9
D) 173
^
^
21) Margin of error: 0.05; confidence level: 95%; p and q unknown
A) 385
B) 419
C) 404
20)
21)
D) 318
Solve the problem. Round the point estimate to the nearest thousandth.
22) Find the point estimate of the proportion of people who wear hearing aids if, in a random sample
of 367 people, 23 people had hearing aids.
A) 0.060
B) 0.937
C) 0.063
D) 0.059
22)
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ.
Assume that the population has a normal distribution.
23) A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly
23)
selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct the 95% confidence interval for the mean score of all such subjects.
A) 64.2 < μ < 88.2
B) 69.2 < μ < 83.2
C) 74.6 < μ < 77.8
D) 67.7 < μ < 84.7
24) The football coach randomly selected ten players and timed how long each player took to perform
a certain drill. The times (in minutes) were:
7.2 10.3 9.7 8.3 11.6
7.3 6.2 11.6 10.4 12.8
Determine a 95% confidence interval for the mean time for all players.
A) 11.14 min < μ < 7.94 min
B) 11.04 min < μ < 8.04 min
C) 7.94 min < μ < 11.14 min
D) 8.04 min < μ < 11.04 min
24)
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
25) Margin of error: $126, confidence level: 95%, σ = $583
25)
A) 72
B) 58
C) 83
D) 116
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Answer Key
Testname: 2014 FALL TEST 3
1)
Because the pattern of the points is curved, it appears that the data do not come from a normally distributed
population.
2) A
3) B
4) B
5) A
6) A
7) A
8) A
9) C
10) B
11) B
12) D
13) D
14) D
15) D
16) D
17) D
18) D
19) C
20) D
21) A
22) C
23) D
24) D
25) C
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