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In a physical fitness test it is known that the probability that a person passes it satisfactorily is 0.80. If 8 people take the test, calculate the probability that at least 4 people fail the test.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

In a physical fitness test it is known that the probability that a person passes it satisfactorily is 0.80. If 8 people take the test, calculate the probability that at least 4 people fail the test.

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Expert Solution

Step 1

$Given n = 8 probability for people fail in test = 1 - 0.80 = 0.20 x ~ Binomial (n = 8, p = 0.20) P (X = x) = (\begin{matrix} n \\ x \end{matrix}) \times p^{x} \times {(1 - p)}^{n - x}; x = 0, 1, . ., np = 0.80$

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