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Q 104.

Expert-verified

The Practice of Statistics for AP

Found in: Page 333

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

An athlete suspected of using steroids is given two tests that operate independently of each other. Test A has a probability $0.9$ of being positive if steroids have been used. Test B has a probability $0.8$ of being positive
if steroids have been used. What is the probability that neither test is positive if steroids have been used?
$(a) 0.72 (c) 0.02 (e) 0.08 (b) 0.38 (d) 0.28$

The correct option is $(c) 0.02$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

P (T e s t A p o s i t i v e) = 0.9 P (T e s t B p o s i t i v e) = 0.8

Step 2. Concept used

Complement rule: $P (A^{c}) = P (n o t A) = 1 - P (A)$

Step 3. Calculation

The complement rule is $P (A^{c}) = P (n o t A) = 1 - P (A)$

Use the complement rule to help you:

P (T e s t A n e g a t i v e) = 1 - P (T e s t A p o s i t i v e) = 1 - 0.9 = 0.1 P (T e s t B n e g a t i v e) = 1 - P (T e s t B p o s i t i v e) = 1 - 0.8 = 0.2

According to the question, the two tests are independent of one another, hence the multiplication rule for independent events can be used:

Fill in the blanks with the corresponding probabilities:

P (N e i t h e r t e s t p o s i t i v e) = P (B o t h t e s t n e g a t i v e) = P (T e s t A n e g a t i v e) \times P (T e s t B n e g a t i v e) = 0.1 \times 0.2 = 0.02

As a result, the proper option is $(c) 0.02$ according to the option.

Most popular questions for Math Textbooks

Income tax returns Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns

in a recent year:

(a) What is the probability that a randomly chosen return shows an adjusted gross income of $$ 50, 000$ or more?

(b) Given that a return shows an income of at least $$ 50, 000,$ what is the conditional probability that the income is at least $$ 100, 000 ?$

Government data show that $8 %$ of adults are full-time college students and that $30 %$ of adults are age $55$ or older. Since $(0.08) (0.30) = 0.024,$ can we conclude that about $2.4 %$ of adults are college students $55$ or older? Why or why not?

Make a two-way table that displays the sample space.

Simulation blunders Explain what’s wrong with each of the following simulation designs.

(a) According to the Centers for Disease Control and Prevention, about $26 %$ of U.S. adults were obese in $2008$ . To simulate choosing $8$ adults at random and seeing how many are obese, we could use two digits. Let $01$ to $26$ represent obese and $27$ to $00$ represents not obese. Move across a row in Table D, two digits at a time, until you find 8 distinct numbers (no repeats). Record the number of obese people selected.

(b) Assume that the probability of a newborn being a boy is $0.5$ . To simulate choosing a random sample of $9$ babies who were born at a local hospital today and observing their gender, use one digit. Use ran dint (0,9) on your calculator to determine how many babies in the sample are male.

Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. How many

students in the sample would need to say “No” to provide convincing evidence that fewer than half of the students at the school brush with the water off? The Fathom dot plot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the

water off is 0.50.

(a) Suppose 27 students in the class’s sample say “No.” Explain why this result does not give convincing evidence that fewer than half of the school’s students brush their teeth with the water off.

(b) Suppose 18 students in the class’s sample say “No.” Explain why this result gives strong evidence that fewer than 50% of the school’s students brush

their teeth with the water off.

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