5.6b Lecture
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Apr 3, 2024
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Section 5.6b
Spring 2022
Normal Distribution Practice
Use any method to answer the questions.
1.
1.
The mean clotting time of blood is 7.45 second, with a
standard deviation of 3.6 second. What is the probability an individual’s blood clotting time will be between 7 and 8 second?
2.
At a major university, exam scores in a large enrollment course are normally distributed with a mean score of 78 and a standard deviation of 6. If the test is curved so that the top 12% of scores receive a grade of A, find the minimum score required for an A.
3.
LSAT scores are normally distributed with a mean of 151 and a standard deviation of 7. Approximately 30% of test takers score below what
number?
4.
The mean batting average in major league baseball is about 0.250. If batting averages are normally distributed, the standard deviation in the averages is 0.03. What percent of batters have an average that is less than 0.300?
5.
A quart of Parker’s milk contains a mean of 39g of butterfat, with a standard deviation of 2g. If the butterfat is normally distributed, find the probability a quart contains more than 40.5 g of butter fat.
6.
The values of mortgage loans made by a certain bank one year were normally distributed with a mean of $120,000 and a standard deviation of $40,000. What is the probability that a randomly selected loan was in the range of $40,000 to $200,000?
7.
A machine produces bolts with an average diameter
of 0.25 inches and a standard deviation of 0.02 inches. What is the probability that a bolt will be produced with a diameter of at least 0.3 inches?
8.
According to the data released by the Chamber of Commerce of a certain city, the weekly wages of factory workers are normally distributed with a mean
of $720 and a standard deviation of $60. What is the MAT 121
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max salary of an employee that earns a wage in the bottom 20%?
A single card is drawn from a standard deck of cards. Find the probability:
9.
The card is red or is an ace
10.
The card is a number card and the card is a spade
11.
The card is a face card or black
12.
The card is a jack and the card is a queen
13.
A diamond and a king
14.
A diamond or a king
15.
A face card and male
16.
Not an ace
17.
Not a black face card
Find the probability of the event if a pair of fair dice is rolled.
18.
The sum is even and both dice are odd
19.
The sum is 7 or 11
20.
The sum is >4 and the sum is < 9
21.
A double or the sum is odd
22.
One die is 6 and the other is < 3
23.
The sum is < 4 or the sum is > 9
24.
Both numbers are odd
25.
The sum is >7 and at least one die is even
26.
The sum is odd or exactly one die is 3
27.
A company’s office of Human Resources reports a breakdown of employees by job type and gender as shown in the table below:
Management
Supervision
Production
Male
7
8
45
Female
6
12
72
What is the probability that a randomly selected employee: a.
Does NOT work in production?
b.
Is female?
c.
Works in management AND is female?
d.
Is male OR works in supervision?
MAT 121
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MAT 121
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33.
As part of a promotional scheme in Arizona and New Mexico, a company distributing frozen foods will award a grand prize
of $100,000 to some person sending in his or her name on an entry blank, with the option of including a label from one of the company’s products. A breakdown of the 225,000 entries received is shown in the following table:
With label
Without label
Arizona
120,000
42,000
New Mexico
30,000
33,000
If the winner of the grand prize is chosen by lot, A
represents the event that it will be won by an entry from Arizona, and L
represents the event that it will be won by an entry which included a label, find each of the following probabilities:
a.
P
(
A
)
b.
P
(
L
)
c.
P
(
A
OR NOT L
)
d.
P
(
NOT
L
AND
A
)
34.
In a study of leadership style and industrial productivity, the following data were obtained:
Leadership Style
Productivity
Democratic (
D
)
Authoritarian (
A
)
Laissez-faire (
F
)
TOTAL
Low (
L
)
40
15
40
95
Medium (
M)
25
75
10
110
High (
H
)
25
30
20
75
TOTAL
90
120
70
280
If one person is to be selected at random, determine the probability the person has the following traits. You do not need to simplify or convert to a decimal.
a.
P
(
M
)
b.
P
(
L
AND
F
)
c.
P
(
H
OR
D
)
d.
P
(
A
)
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MAT 121
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Find the missing probability.
35. Find P
(
A∩ B
)
if P
(
A
)
=
0.3
, P
(
B
)
=
0.65
, P
(
A
∪
B
)
=
0.755
36. Find P
(
B
)
if P
(
A '
)
=
0.65
,P
(
A
∪
B
)
=
0.89
,P
(
A ∩B
)
=
0.21
37. Find P
(
A'
)
if P
(
B
)
=
0.25
, P
(
A
∪
B
)
=
0.625
, P
(
A ∩ B
)
=
0.115
38. Find P
(
A
∪
B
)
if P
(
A
)
=
0.5
, P
(
B'
)
=
0.25
, P
(
A ∩B
)
=
0.375
39. Find P
(
A ∩ B
)
'
if P
(
A
)
=
0.25
, P
(
B
)
=
0.55
, P
(
A
∪
B
)
=
0.6625
40. Find P
(
A
∪
B
)
'
if P
(
A
)
=
0.45
, P
(
B
)
=
0.6
, P
(
A∩ B
)
=
0.27
MAT 121
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