The actual proportion of families in a certain city who own their home is 0.68. If 84 families in this city are interviewed at random and their responses to the question of whether they own their home are looked upon as values of independent random variables having identical Bernoulli distributions with parameter θ = 0.68, with what approximate probability can we assert that the value we obtain for the sample proportion will fall between 0.65 and 0.70, based on the central limit theorem?
The actual proportion of families in a certain city who own their home is 0.68. If 84 families in this city are interviewed at random and their responses to the question of whether they own their home are looked upon as values of independent random variables having identical Bernoulli distributions with parameter θ = 0.68, with what approximate probability can we assert that the value we obtain for the sample proportion will fall between 0.65 and 0.70, based on the central limit theorem?
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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The actual proportion of families in a certain city who own their home is
0.68. If 84 families in this city are interviewed at random and their responses to the question of
whether they own their home are looked upon as values of independent random variables having
identical Bernoulli distributions with parameter θ = 0.68, with what approximate probability
can we assert that the value we obtain for the sample proportion will fall between 0.65 and
0.70, based on the central limit theorem?
Expert Solution
Step 1
We have given that,
The random variable having a independent and identical distributed Bernoulli random variable with parameter .
The actual proportion of families in a certain city who own their home is .
Also in that city randomly selected families are interviewed and collected their response. i.e. .
if
Then mean and variance of Bernoulli distribution is
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