**Math 210 - Module 6: Sampling Distribution of Proportions**This module covers the sampling distribution of proportions, which is normal under certain conditions.**Mean and Standard Deviation:**- The mean ($ \mu_{\hat{p}} $) of the sampling distribution is equal to the population proportion ($ p $).- The standard deviation ($ \sigma_{\hat{p}} $) is given by: \[ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \]**Example Problem:**Assume the conditions are met. Suppose a weighted coin has a 44.0% chance of getting heads. Use the normal distribution to find the probability that when flipping the coin 110 times, the proportion of heads is more than 50.0%.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Section: Chapter Questions

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**Math 210 - Module 6: Sampling Distribution of Proportions**

This module covers the sampling distribution of proportions, which is normal under certain conditions.

**Mean and Standard Deviation:**

- The mean ($ \mu_{\hat{p}} $) of the sampling distribution is equal to the population proportion ($ p $).
- The standard deviation ($ \sigma_{\hat{p}} $) is given by:
\[
\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}
\]

**Example Problem:**

Assume the conditions are met. Suppose a weighted coin has a 44.0% chance of getting heads. Use the normal distribution to find the probability that when flipping the coin 110 times, the proportion of heads is more than 50.0%.

Expert Solution

Step 1: Write the given information.

Given information:

$mu subscript p with hat on top end subscript equals p sigma subscript p with hat on top end subscript equals square root of fraction numerator p open parentheses 1 minus p close parentheses over denominator n end fraction end root$

p=The chance of getting heads= 44.0%=0.44

n=number of coins flipped = 110

Therefore,

$mu subscript p with hat on top end subscript equals p equals 0.44 sigma subscript p with hat on top end subscript equals square root of fraction numerator p open parentheses 1 minus p close parentheses over denominator n end fraction end root equals square root of fraction numerator 0.44 open parentheses 1 minus 0.44 close parentheses over denominator 110 end fraction end root equals 0.047329$