Consider the production data shown in this example. (Assume a normal distribution. Due to the nature of this problem, (a) What is the mean (in minutes)? x = 9.22 minutes (b) What is the standard deviation (in minutes)? 515.16 S Z 99 X-X S 2.2811 (c) Determine the z value corresponding to a 5-minute-assembly time. 59.22 2.2811 minutes -1.85
Consider the production data shown in this example. (Assume a normal distribution. Due to the nature of this problem, (a) What is the mean (in minutes)? x = 9.22 minutes (b) What is the standard deviation (in minutes)? 515.16 S Z 99 X-X S 2.2811 (c) Determine the z value corresponding to a 5-minute-assembly time. 59.22 2.2811 minutes -1.85
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:EXAMPLE
In order to improve the production time, the supervisor of assembly lines
for a computer manufacturer has studied the time that it takes to assem-
ble certain parts of a computer at various stations. She measures the time
that it takes to assemble a specific part by 100 people at different shifts
and on different days. The record of her study is organized and shown
in the table below.
Based on data provided, we have calculated the probabilities correspond-
ing to the time intervals that people took to assemble the parts. The
probability distribution for this example is shown in the table below and
the following figure.
Data Pertaining to this example
Time That It Takes a Person to
Assemble the Part (minutes)
5
Probability
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
6
5 6
7
8
9
10
AWN ==
11
12
13
14
Frequency
5
8
11
15
17
14
13
8
6
3
Σ=100
Again, note that the sum of probabilities is equal to 1. Also note that
if we were to connect the midpoints of time results (as shown in the figure
below), we would have a curve that approximates a bell shape. As the
number of data points increases and the intervals decrease, the
probability-distribution curve becomes smoother. A probability
distribution that has a bell-shaped curve is called a normal distribution.
The probability distribution for many engineering experiments is
approximated by a normal distribution.
7 8 9 10 11 12 13 14
Time (minutes)
Plot of probability distribution for this example.
Probability
(P)
0.05
0.08
0.11
0.15
0.17
0.14
0.13
0.08
0.06
0.03
Σp=1
Transcribed Image Text:Consider the production data shown in this example. (Assume a normal distribution. Due to the nature of this problem,
(a) What is the mean (in minutes)?
x = 9.22
minutes
(b) What is the standard deviation (in minutes)?
515.16
S =
Z =
X-X
S
99
(c) Determine the z value corresponding to a 5-minute-assembly time.
5- 9.22
= -1.85
2.2811
=
2.2811
minutes
(d) Referring to this table, determine the A value.
A =
(e) Determine the probability that it will take a person longer than 5 minutes to assemble the computer parts.
0.5 +
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON