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Q. 50

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Introductory Statistics

Found in: Page 387

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

Use the following information to answer the next four exercises:
$X ~ N (54, 8)$
Find the probability that $x > 56 .$

The probability that $x > 56$ is $0.4013$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

Given in the question that,

$X ~ N (54, 8)$

We have to find the probability that $x > 56$

Step 2: Explanation

According to the given information, we can compute the probability as follow:

$p (X > 56) = 1 - p (X \leq 56)$

$= 1 - p (Z \leq \frac{X - μ}{σ})$

$= 1 - p (Z \leq \frac{56 - 54}{8})$

$= 1 - p (Z \leq 0.25)$

Step 3: Apply the probability rule

Apply the probability rule to compute the value of $P (Z \leq 0.25)$

$P (Z \leq a) = P (Z \leq 0) + P (0 \leq Z \leq a)$

$a = 0.25$

$= P (Z \leq 0) + P (0 \leq Z \leq 0.25)$

$P (Z \leq 0) = 0.5$

Cumulative probability of $P (0 \leq Z \leq 0.25)$ :

$= 0.5 + 0.0987$

$= 0.5987$

Step 4: Place the value

Place the value of $P (Z \leq 2.5)$ in the above formula

$p (X > 56) = 1 - p (Z \leq 0.25)$

$= 1 - 0.5987$

$= 0.4013$

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