A livestock company reports that the mean weight of a group of young steers is1142pounds with a standard deviation of79pounds. Based on the modelN(1142,79)for the weights of steers, what percent of steers weigha) over1050pounds?b) under1200pounds?

Name: A livestock company reports that the mean weight of a group of young s
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Description: A livestock company reports that the mean weight of a group of young steers is1142pounds with a standard deviation of79pounds. Based on the modelN(1142,79)for the weights of steers, what percent of steers weigha) over1050pounds?b) under1200po

Answered: A livestock company reports that 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

A livestock company reports that the mean weight of a group of young steers is

1142

pounds with a standard deviation of

pounds. Based on the model

N(1142,79)

for the weights of steers, what percent of steers weigh

a) over

1050

pounds?

b) under

1200

pounds?

Expert Solution

Step 1

Let X be a random variable such that

X: Weight of a young steer

$X ~ N (1142, 79^{2})$

The probability of weight of a steer being over 1050 pounds is given by

$P (X > 1050) = P (\frac{X - μ}{σ} > \frac{1050 - 1142}{79}) = P (Z > - 1.1645) = 1 - P (Z \leq - 1.1645)$

Using Excel,

Therefore,

Therefore, the probability of weight of a steer being over 1050 pounds is 0.8778

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