Answered: a) Find the probability of existence of…

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

Wild boar population weight has standard deviation of 50 lb.

a) Find the probability of existence of a random sample (size 100) weight within + 5 lb. of population mean weight.

b) For the same sample size, find the probability of the weight within + 10 lb. of population mean weight.

Expert Solution

Step 1

Wild boar population weight has standard deviation of 50 lb. That is, $σ = 50$ .

The probability of existence of a random sample (size 100) weight within $\pm$ 5 lb. of population mean weight is,

$\begin{array}{rcl} P (- 5 < \bar{x} - μ < 5) & = & P (\frac{- 5}{(\frac{50}{\sqrt{100}})} < \frac{\bar{x} - μ}{(\frac{σ}{\sqrt{n}})} < \frac{5}{(\frac{50}{\sqrt{100}})}) \\ = & P (\frac{- 5}{5} < z < \frac{5}{5}) \\ = & P (- 1 < z < 1) \\ = & P (z < 1) - P (z < - 1) \end{array}$

The probability of z less than –1 can be obtained using the excel formula “=NORM.S.DIST(–1,TRUE)”. The probability value is 0.1587.

The probability of z less than 1 can be obtained using the excel formula “=NORM.S.DIST(1,TRUE)”. The probability value is 0.8413.

The required probability value is,

$\begin{array}{rcl} P (- 5 < \bar{x} - μ < 5) & = & P (z < 1) - P (z < - 1) \\ = & 0.8413 - 0.1587 \\ = & 0.6826 \end{array}$

Thus, the probability of existence of a random sample (size 100) weight within $\pm$ 5 lb. of population mean weight is 0.6826.

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