Answered: n a certain city of several million…

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

In a certain city of several million people, 7.8% of the adults are unemployed. If a random sample of 250 adults in this city is selected, approximate the probability that fewer than 16 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity.

Round your answer to at least three decimal places. Do not round any intermediate steps.

Expert Solution

Step 1

Given Information:

7.8% of the adults are unemployed. i.e.., $p = 0.078$

Sample size $n = 250$

To find the probability that fewer than 16 in the sample are unemployed.

Let X denote the number of adults who are unemployed and X follows Binomial distribution with parameters $n = 250$ and $p = 0.078$ .

Mean $μ = n p = 250 (0.078) = 19.5$

Standard deviation is calculated using the formula:

$\begin{array}{rcl} σ & = & \sqrt{n p (1 - p)} \\ = & \sqrt{250 (0.078) (1 - 0.078)} \\ = & 4.240165091 \end{array}$

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