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Q.10

Expert-verified

The Practice of Statistics for AP

Found in: Page 410

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

A test for extrasensory perception (ESP) involves asking a person to tell which of $5$ shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the $5$ shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first $4$ shapes incorrectly but gets the fifth correct?
a). $1 / 5$
b). ${(\frac{4}{5})}^{4}$
c). ${(\frac{4}{5})}^{4} (\frac{1}{5})$
d). $(\frac{5}{1}) {(\frac{4}{5})}^{4} (\frac{1}{5})$
e). $4 / 5$

A correct answer is an option (c) ${(\frac{4}{5})}^{4} (\frac{1}{5})$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

A test for extrasensory perception (ESP) involves asking a person to tell which of $5$ shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen.

Step 2: Explanation

The number of positive outcomes divided by the total number of possible outcomes equals the probability:

$p = P (w i n) = \frac{# of favorable outcomes}{# of possible outcomes} = \frac{1}{5}$

Because the variable represents the number of tries required before a success, the distribution is geometric.

Geometric probability is defined as follows:

$P (X = k) = q^{k - 1} p = (1 - p)^{k - 1} p$

Evaluate at $k = 5$ :

$P (X = 5) = {(1 - \frac{1}{5})}^{5 - 1} (\frac{1}{5}) = {(\frac{4}{5})}^{4} (\frac{1}{5})$

Most popular questions for Math Textbooks

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7. Benford’s law Refer to Exercise 5. The first digit of a randomly chosen expense account claim follows Benford’s law. Consider the events A = first digit is 7 or greater and B = first digit is odd.

(a) What outcomes make up the event A? What is P(A)?

(b) What outcomes make up the event B? What is P(B)?

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(c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company’s $1$ -in- $6$ claim inaccurate? Compute $P (X \geq 3)$ and use the result to justify your answer.

Based on the analysis in Exercise $41$ , the ferry company decides to increase the cost of a trip to $$ 6$ . We can calculate the company’s profit $Y$ on a randomly selected trip from the number of cars $X$ . Find the mean and standard deviation of $Y$ . Show your work.

Friends How many close friends do you have? An opinion poll asks this question of an SRS of $1100$ adults. Suppose that the number of close friends adults claim to have varies from person to person with mean $μ = 9$ and standard deviation $σ = 2.5$ . We will see later that in repeated random samples of size 1100, the mean response x will vary according to the Normal distribution with mean $9$ and standard deviation $0.075$ . What is role="math" localid="1649504967961" $P (8.9 \leq x \leq 9.1)$ , the probability that the sample result x estimates the population truth $μ = 9$ to within $\pm 0.1$ ?

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