October 29, 2013
Exam II
VERSION A
Put ALL answers on the ANSWER SHEET
Name________________________
Class________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Identify the given random variable as being discrete or continuous.
1) The number of oil spills occurring off the Alaskan coast
1) _______
A) Continuous
B) Discrete
Find the mean of the given probability distribution.
2)
A) μ = 2.42
B) μ = 2.16
2) _______
C) μ = 2.26
D) μ = 2.52
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The
probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question
using the table.
Probabilities of Girls
3) Find the probability of selecting exactly 8 girls.
A) 0.183
B) 0.000
3) _______
C) 0.122
D) 0.022
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial. Round to three
decimal places.
4) n = 7, x = 4 , p = 0.5
4) _______
A) 0.273
B) 0.355
C) 0.410
D) 0.063
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest
tenth.
5) n = 38; p = 0.2
5) _______
A) μ = 8.3
B) μ = 7.6
C) μ = 7.1
D) μ = 7.9
Math 155
10/29/13
VERSION A
1
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
6)
6) _______
A) 0.8907
B) 0.1292
C) 0.8708
D) 0.8485
7)
7) _______
A) 0.8212
B) 0.3576
C) 0.1788
D) 0.6424
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
8) Shaded area is 0.9599.
8) _______
A) 1.03
B) 1.75
C) 1.82
If z is a standard normal variable, find the probability.
9) The probability that z lies between 0 and 3.01
A) 0.4987
B) 0.9987
D) -1.38
9) _______
C) 0.5013
D) 0.1217
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of
at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water,
some give readings below
(denoted by negative numbers) and some give readings above
(denoted by
positive numbers). Assume that the mean reading is
and the standard deviation of the readings is
Also
assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly
selected and tested. Find the temperature reading corresponding to the given information.
10) Find P96, the 96th percentile.
10) ______
A) -1.38°
B) 1.75°
C) 1.03°
D) 1.82°
Find the indicated value.
11) .005
11) ______
z
A) 2.015
Math 155
10/29/13
B) 2.835
C) 2.575
VERSION A
D) 2.535
2
Find the indicated probability.
12) The diameters of bolts produced by a certain machine are normally distributed with a mean of
0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter
greater than 0.32 inches?
A) 37.45%
B) 2.28%
C) 47.72%
D) 97.72%
Solve the problem.
13) Scores on a test have a mean of 67 and Q3 is 83. The scores have a distribution that is
approximately normal. Find the standard deviation. Round your answer to the nearest tenth.
A) 23.9
B) 21.3
C) 10.7
D) 12
12) ______
13) ______
The given values are discrete. Use the continuity correction and describe the region of the normal distribution that
corresponds to the indicated probability.
14) The probability of more than 44 correct answers
14) ______
A) The area to the right of 43.5
B) The area to the right of 44.5
C) The area to the left of 44.5
D) The area to the right of 44
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
15) With n = 20 and p = 0.60, estimate P(fewer than 8).
15) ______
A) 0.4332
B) 0.0668
C) 0.0202
D) 0.4953
Find the indicated critical z value.
16) Find the critical value
A) 2.33
that corresponds to a 98% confidence level.
B) 1.75
C) 2.05
Express the confidence interval using the indicated format.
17)
Express the confidence interval 0.039 < p < 0.479 in the form of
± E.
A) 0.22 ± 0.5
B) 0.259 ± 0.5
C) 0.259 ± 0.22
16) ______
D) 2.575
17) ______
D) 0.259 - 0.22
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
18) 95% confidence; n = 380, x = 50
18) ______
A) 0.0306
B) 0.0357
C) 0.0408
D) 0.0340
Solve the problem. Round the point estimate to the nearest thousandth.
19) Find the point estimate of the proportion of people who wear hearing aids if, in a random sample
of 898 people, 46 people had hearing aids.
A) 0.949
B) 0.049
C) 0.051
D) 0.050
19) ______
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.
20) n = 10, = 8.1, s = 4.8, 95% confidence
20) ______
A) 4.67 < μ < 11.53
B) 4.68 < μ < 11.52
C) 4.72 < μ < 11.48
D) 5.32 < μ < 10.88
21) Thirty randomly selected students took the calculus final. If the sample mean was 95 and the
standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.
A) 91.69 < μ < 99.31
B) 92.95 < μ < 97.05
C) 91.68 < μ < 98.32
D) 92.03 < μ < 97.97
Math 155
10/29/13
VERSION A
21) ______
3
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
22) Margin of error: $135, confidence level: 95%, σ = $500
22) ______
A) 46
B) 74
C) 37
D) 53
23) How many students must be randomly selected to estimate the mean weekly earnings of students
at one college? We want 95% confidence that the sample mean is within $2 of the population
mean, and the population standard deviation is known to be $60.
A) 2435
B) 3047
C) 4886
D) 3458
Do one of the following, as appropriate: (a) Find the critical value
, (b) find the critical value
neither the normal nor the t distribution applies.
24) 98%; n = 7; σ = 27; population appears to be normally distributed.
A)
B)
C)
D)
= 2.575
= 1.96
= 2.05
= 2.33
If z is a standard normal variable, find the probability.
25) The probability that z lies between -1.10 and -0.36
A) 0.4951
B) 0.2237
Math 155
10/29/13
VERSION A
23) ______
, (c) state that
24) ______
25) ______
C) -0.2237
D) 0.2239
4
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
B
C
A
A
B
C
D
B
A
B
C
B
A
B
C
A
C
D
C
A
C
D
D
D
B
Math 155
10/29/13
VERSION A
5