According to a survey, 10% of Americans are afraid to fly. Suppose 1,100 Americans are sampled.a. What is the probability percentage that 121 or more Americans in the survey are afraid to fly? Round the percent to two decimal places. [Text Box for Input]b. What is the probability percentage that 165 or more Americans in the survey are afraid to fly? Round the percent to two decimal places. [Text Box for Input]c. What is the probability percentage that 8% or less of the Americans surveyed answered they were afraid to fly? Round the percent to two decimal places. [Text Box for Input]Question Help: Video [Link] Submit Question [Button]

Answered: According to a survey, 10% of Americans…

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

According to a survey, 10% of Americans are afraid to fly. Suppose 1,100 Americans are sampled.

a. What is the probability percentage that 121 or more Americans in the survey are afraid to fly? Round the percent to two decimal places.
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b. What is the probability percentage that 165 or more Americans in the survey are afraid to fly? Round the percent to two decimal places.
[Text Box for Input]

c. What is the probability percentage that 8% or less of the Americans surveyed answered they were afraid to fly? Round the percent to two decimal places.
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Expert Solution

Step 1

It is given that $n = 1100 a n d p = 10 % = 0.1$ .
Let X be the number of people who are afraid to fly.

Now, the mean is
$\begin{array}{rcl} μ & = & n p \\ = & 1100 \times 0.1 \\ = & 110 \end{array}$

And the standard deviation is
$\begin{array}{rcl} σ & = & \sqrt{n p (1 - p)} \\ = & \sqrt{110 (0.9)} \\ = & 9.94987 \end{array}$

Step 2

a)
The z-score is calculated as
$\begin{array}{rcl} z & = & \frac{x - μ}{σ} \end{array}$

Then,
$\begin{array}{rcl} P (X \geq 121) & = & 1 - P (X < 121) \\ = & 1 - P (\frac{X - μ}{σ} < \frac{x - μ}{σ}) \\ = & 1 - P (Z < \frac{121 - 110}{9.94987}) \\ = & 1 - P (Z < 1.10) F r o m t h e l e f t t a i l e d t a b l e s \\ = & 1 - 0.8643 \\ = & 0.1357 \\ = & 13.57 % \end{array}$