Q. 8 T6.8. Seventeen people have been... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 6: Q. 8 (page 409)

T6.8. Seventeen people have been exposed to a particular disease. Each one independently has a $40 %$ chance of contracting the disease. A hospital has the capacity to handle $10$ cases of the disease. What is the probability that the hospital鈥檚 capacity will be exceeded?
(a) $0.011$ (b) $0.035$ (c) $0.092$ (d) $0.965$ (e) $0.989$

Short Answer

Expert verified

The probability of the hospital's capacity will be exceeded is $0.035$ . So, the option (b) is correct.

Step by step solution

Given information

A hospital has the capacity to handle $10$ cases of the disease. Each one independently has a $40 %$ chance of contracting the disease.

Explanation

Let, Sample size $n = 17$
Probability of success $p = 40 % = 0.40$
Definition binomial probability:
$P (X = k) = (\begin{array}{l} n \\ k \end{array}) 路 p^{k} 路 {(1 - p)}^{n - k}$
Evaluate $k = 11, 12, 13, 14, 15, 16, 17$ :

P (X = 11) = (\begin{matrix} 17 \\ 11 \end{matrix}) 鈰� {0.40}^{11} 鈰� (1 鈭� 0.40)^{17 鈭� 11} 鈮� 0.0242

$P (X = 12) = (\begin{matrix} 17 \\ 12 \end{matrix}) 鈰� {0.40}^{12} 鈰� (1 鈭� 0.40)^{17 鈭� 12} 鈮� 0.0081$

$P (X = 13) = (\begin{matrix} 17 \\ 13 \end{matrix}) 鈰� {0.40}^{13} 鈰� (1 鈭� 0.40)^{17 鈭� 13} 鈮� 0.0021$

$P (X = 14) = (\begin{matrix} 17 \\ 14 \end{matrix}) 鈰� {0.40}^{14} 鈰� (1 鈭� 0.40)^{17 鈭� 14} 鈮� 0.0004$

$P (X = 15) = (\begin{matrix} 17 \\ 15 \end{matrix}) 鈰� {0.40}^{15} 鈰� (1 鈭� 0.40)^{17 鈭� 15} 鈮� 0.0001$

$P (X = 16) = (\begin{matrix} 17 \\ 16 \end{matrix}) 鈰� {0.40}^{16} 鈰� (1 鈭� 0.40)^{17 鈭� 16} 鈮� 0.0000$

$P (X = 17) = (\begin{matrix} 17 \\ 17 \end{matrix}) 鈰� {0.40}^{17} 鈰� (1 鈭� 0.40)^{17 鈭� 17} 鈮� 0.0000$

Then, the probabilities as:

$= P (X = 11) + P (X = 12) + P (X = 13) + . . . . . . . . . + P (X = 16) + P (X = 17)$

$= 0.0242 + 0.0081 + 0.0021 + 0.0004 + 0.0001 + 0.0000 + 0.0000$

$= 0.0348 鈮� 0.035$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.