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Q.1

Expert-verified

The Practice of Statistics for AP

Found in: Page 353

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

Toss $4$ times Suppose you toss a fair coin $4$ times. Let $X =$ the number of heads you get.
(a) Find the probability distribution of $X$ .
(b) Make a histogram of the probability distribution. Describe what you see.
(c) Find $P (X \leq 3)$ and interpret the result.

(a)Probability distribution of $X$ is

(b)

(c) $P (X \leq 3) = 93.75 %$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1: Given information

Given in the question that , you toss a fair coin $4$ times. Let $X$ = the number of heads you get

We need to find the probability distribution of $X$ .

Part (a) Step 2: Explanation

If $H$ is heads and $T$ is tails, there are $16$ different ways to throw the fair coin four times:

Each of these outcomes has an equal chance of occurring $\frac{1}{16}$ .

The product of the number of related outcomes and the probability yields the probability distribution of $X =$ "the number of heads":

$x$	$0$	$1$	$2$	$3$	$4$
$P (X = x)$	$\frac{1}{6}$	$\frac{4}{16}$	$\frac{6}{16}$	$\frac{4}{16}$	$\frac{1}{16}$

Part (b) Step 3: Given information

Given in the question that , you toss a fair coin 4 times. Let X = the number of heads you get

We need to make a histogram of the probability distribution.

Step 4: Explanation(part b)

Consider the given table:

Each bar's width must be equal, and its height must be equal to the probability:

The histogram is around 2 degrees symmetric.

Part (c) Step 1: Given information

Given in the question that, you toss a fair coin $4$ times. Let $X$ = the number of heads you get.

We need to find $P (X \leq 3)$ .

Part (c) Step 2: Explanation

Consider the given table:

Let's add the corresponding probabilities

$P (X \leq 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = \frac{1}{16} + \frac{4}{16} + \frac{6}{16} + \frac{4}{16} = 0.9375$

We should expect to get $3$ heard or less in around $93.75$ or $94$ of the $100$ times we perform the quadruple toss of the coin.

Most popular questions for Math Textbooks

80. More lefties Refer to Exercise 72.

(a) Find the probability that exactly $3$ students in the sample are left-handed. Show your work.(b) Would you be surprised if the random sample contained $4$ or more left-handed students? Compute $P (W \geq 4)$ and use this result to support youranswer.

The standard deviation of $T$ is

(a) $22$

(b) $16$

(c) $15.62$

(d) $11.66$

(e) $4$

Binomial setting? A binomial distribution will be approximately correct as a model for one of these two sports settings and not for the other. Explain why by briefly discussing both settings. (a) A National Football League kicker has made $80 %$ of his field-goal attempts in the past. This season he attempts $20$ field goals. The attempts differ widely in the distance, angle, wind, and so on. (b) A National Basketball Association player has made $80 %$ of his free-throw attempts in the past. This season he takes $150$ free throws. Basketball free throws are always attempted from $15$ feet away with no interference from other players

$\begin{array}{lcccccccc} Days & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ Probability & 0.68 & 0.05 & 0.07 & 0.08 & 0.05 & 0.04 & 0.01 & 0.02 \end{array}$

Working out Refer to Exercise 6. Consider the events A = works out at least once and B = works out less than 5 times per week.

(a) What outcomes makeup event A? What is P(A)?

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

(c) What outcomes make up the event “A and B”? What is P(A and B)? Why is this probability not equal to P(A) · P(B)?

Ana is a dedicated Skee Ballplayer (see photo) who always rolls for the $50$ -point slot. The probability distribution of Ana's score $X$ on a single roll of the ball is shown below. You can check that $μ_{X} = 23.8$ and $σ_{X} = 12.63$ .

(a) A player receives one ticket from the game for every $10$ points scored. Make a graph of the probability distribution for the random variable $T =$ number of tickets Ana gets on a randomly selected throw. Describe its shape.

(b) Find and interpret $μ_{T}$ .

(c) Compute and interpret $σ_{T}$ .

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