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Fall 2010
Math 227
Final
Name: ______________________
Show your work clearly, neatly, and understandably. Make sure you round the decimal for probability to 5-decimal place and round
the percentage to 3-decimal.
1.
Lengths of salmon caught by fishermen
in Alaska are normally distributed with a mean
of 21.5 inches and a standard deviation of 3.25
inches.
a. (2) What percentages of the salmon are
longer than 20.40 inches?
(Total 17)
b.
(3) The
percentage of the salmon shorter
than k inches is 85%. Find k.
c.
(3) A sample
of 10 salmon is selected at
random. What is the probability that 3 of
them have length more than 20.40 inches?
d.
(4)
Find the probability that the average
length of 10 randomly selected salmon is
between 24 in and 25 in.
e.
(5) Find
the probability that, of 100 salmon,
more than 55 with length more than 20.40
inches.
2.
(Total 8) A box
contains 9 identical balls (except
in colors): 3 red, 4 yellow, and 2 green.
a.
(3)
Three balls are selected without
replacement. Find the probability of
selecting 2 or more red balls.
b.
(5)
Create a probability distribution of the
number of yellow balls selected for a
procedure of selecting three balls without
replacement.
3.
The chips of a computer manufacturer
are supplied by 3 companies: 40% from A,
(Total 10)
35% from B, and the rest by C. Of those
supplied by A, 1% are defective; by B, 2% are
defective; by C, 4% are defective.
a. (3) A chip is randomly selected. Find the
probability that the chip is defective.
b.
(3)
Given a chip is defective. Find the
probability that the chip is from A.
c.
(4)
Out of 100 defective chips, find the
probability that less than 25 are from
company A.
4.
(Total 5)
Suppose P(A) = 0.57, P(B) = 0.74, and
b.
(6)
Construct 95%-CI for mean.
c.
(8) At
P(AB) = 0.95. Find:
5.
a.
(3)
P(AB)
b.
(2)
P(A|B)
(Total 5) Suppose
P(A) = 0.57, P(B) = 0.60, and
P(A|B) = 0.75.
6.
a.
(3)
P(AB)
b.
(2)
P(AB)
(Total 20) Suppose
that the weight of the cereal in
boxes of Loopy Froots breakfast cereal is
normally distributed. A consumer advocate
group randomly sampled 8 boxes of Loopy
Froots and weighed the contents (in grams):
535, 540, 565, 575, 535, 558, 564, and 550.
a.
Find the mean and standard deviation
of the sample.
(2,4)
5%-SL, test the claim that the weight
of the cereal in boxes of Loopy Froots
breakfast is less than 570 grams.
7.
(Total 18) A course
is offered by the Mathematics Department in two sections taught by two different
instructors, whose grade distributions are approximately normal. Data from the past is summarized in the
following:
Mr. X: number of students = 56, number of passing students = 25,
Average class X = 68, standard deviation x = 21
Ms. Y: number of students = 78, number of passing students = 52,
Average class Y = 70, standard deviation y= 12
a. (8) At 5%-SL, test the claim that Ms. Y’s class has a higher passing rate.
b.
(10) At
5%-SL, test the claim that Ms. Y’s class has a higher average.
8.
(Total 26)
The following are the Test 3 scores of all my PreAlgebra classes at WLAC.
From the data, find:
10
38
49
59
74
84
98
15
40
51
59
77
88
100
18
42
51
67
78
89
104
20
43
52
68
79
89
107
22
43
52
69
80
90
23
44
53
69
80
91
24
44
55
69
80
92
26
45
56
69
80
92
36
46
58
69
83
93
37
48
59
71
84
96
a.
(2)
Median
b.
(2)
Mode
c.
(2)
Q1
d.
(2)
Q3
e.
(1)
Range
Data are sorted and rounded to the nearest unit for simplicity.
f.
(10)
g.
(7)
Create a Frequency Distribution with 6 classes and extend to estimate the mean and standard deviation.
Create a 95%-CI for the standard deviation.
9.
(3)
The Los Angeles Beanstalk Club has a height requirement that women must be at least 68 in. tall.
Women’s heights are normally distributed with a mean of 63.6 in. and a standard deviation of 2.5 in. What
percentages of women meet that requirement? Draw a density curve with all relevant information.