Answered: Please explain to me where did the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Please explain to me where did the circled answer ( 0.1265) come from. Thanks! Here’s the problem: The seasonal output of new experimental strain of pepper plants was carefully weighted. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

4:10
←
Step1
a)
According to the provided information,
Mean (μ)=15
Standard Deviation (o)=1.75
Step2
b)
The estimate produced peppers weighing
between 13 and 16 pounds can be calculated
as:
P(13< X <16)=P(13-15<X-μ<16-15)
(13-15 X-u 16-15
1.75
σ
1.75
= P
=P(-1.1429 <Z <0.5714)
=P(0.5714)-P(-1.1429)
P(-1.1429)=1-P(1.1429)
0.1265
P(13< X<16)=0.7161-0.1265
= 0.5896
Estimate produced peppers weighing
between 13 and 16 pounds
= 200 x 0.5896
?
LTE 16
= 117.9 Plants
Therefore, the estimate produced peppers
weighing between 13 and 16 pounds is
117.9
√x
DO

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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