MM207 Unit 5: Normal Distribution, Probabilities, and Sampling Distributions
Examines normal distribution and sampling techniques.
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MM207 Unit 5 Chapter 5 Project
ROBYN GALINDO
1
MM207 Unit 5: Normal Distribution, Probabilities, and Sampling
Distributions
Total points are 40. Points are included with each problem.
Included with each section or problem are reference examples and end of section
exercises that can be used as a guide. Be sure to show your work in case partial
credit is awarded. To receive full credit, work must be shown if applicable.
Section 5.1: Introduction to Normal Distribution and the Standard Normal
Distribution
1. Use the Standard Normal Distribution table to find the indicated area under the
standard normal curve.
(References: example 3 - 6 pages 244 - 247, end of section exercises 21 –
40 page 249) (2 points per each part)
a. Between z = 0 and z = 1.42
The area to the left of z = 0 is 0.5000.
The area to the left of z = 1.42 is 0.9222.
The area between z = 0 and z = 1.42 is 0.4222.
b. To the left of z = 1.86
The area to the left of z = 1.86 is 0.9686.
c. Between z = -1.52 and z = -0.46
The area to the left of z = -1.52 is 0.0643.
The area to the left of z = -0.46 is 0.3228.
The area between z = -1.52 and z = -0.46 is 0.2585.
d. To the right of z = -1.45
The area to the right of z = -1.45 is 1 - .0735 = 0.9265.
Section 5.2: Normal Distributions: Find Probabilities
(References: example 1 and 2 page 253, end of section exercises 13 - 30
pages 257 - 259
2. The diameters of a wooden dowel produced by a new machine are
normally distributed with a mean of 0.55 inches and a standard deviation of
0.01 inches. What percent of the dowels will have a diameter less than 0.56?
(6 points)
Z = (0.56 – 0.55) / .01 = 1 = 0.8413
84.13% of the dowels will have a diameter of less than 0.56.
ROBYN GALINDO
1
MM207 Unit 5: Normal Distribution, Probabilities, and Sampling
Distributions
Total points are 40. Points are included with each problem.
Included with each section or problem are reference examples and end of section
exercises that can be used as a guide. Be sure to show your work in case partial
credit is awarded. To receive full credit, work must be shown if applicable.
Section 5.1: Introduction to Normal Distribution and the Standard Normal
Distribution
1. Use the Standard Normal Distribution table to find the indicated area under the
standard normal curve.
(References: example 3 - 6 pages 244 - 247, end of section exercises 21 –
40 page 249) (2 points per each part)
a. Between z = 0 and z = 1.42
The area to the left of z = 0 is 0.5000.
The area to the left of z = 1.42 is 0.9222.
The area between z = 0 and z = 1.42 is 0.4222.
b. To the left of z = 1.86
The area to the left of z = 1.86 is 0.9686.
c. Between z = -1.52 and z = -0.46
The area to the left of z = -1.52 is 0.0643.
The area to the left of z = -0.46 is 0.3228.
The area between z = -1.52 and z = -0.46 is 0.2585.
d. To the right of z = -1.45
The area to the right of z = -1.45 is 1 - .0735 = 0.9265.
Section 5.2: Normal Distributions: Find Probabilities
(References: example 1 and 2 page 253, end of section exercises 13 - 30
pages 257 - 259
2. The diameters of a wooden dowel produced by a new machine are
normally distributed with a mean of 0.55 inches and a standard deviation of
0.01 inches. What percent of the dowels will have a diameter less than 0.56?
(6 points)
Z = (0.56 – 0.55) / .01 = 1 = 0.8413
84.13% of the dowels will have a diameter of less than 0.56.
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Document Details
University
Kaplan University School of Business and Management
Subject
Mathematics