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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

DISCUSS: Most Likely Outcome for n Tosses of a Coin A balanced coin is tossed n times. In this exercise we investigate the following question: What is the number of heads that has the greatest probability of occurring? Note that for a balanced coin the probability of heads is p = 0.5 .

(a) Suppose n = 8 . Draw a probability histogram for the resulting binomial distribution. What number of heads has the greatest probability of occurring? If n = 100 , what number of heads has the greatest probability of occurring?

(b) Suppose n = 9 . Draw a probability histogram for the resulting binomial distribution. What number of heads has the greatest probability of occurring? If n = 101 , what number of heads has the greatest probability of occurring?

To determine

(a)

To find:

The number of heads that have the greatest probability of occurring when a coin is tossed n times, draw a probability histogram for n=8 and find the number of heads that have the greatest probability of occurring for n=100.

Explanation

Given:

A balanced coin is tossed n times.

For a balanced coin, the probability of heads is p=0.5.

Approach:

Use excel to draw a probability histogram for n tosses of a coin and the formula for binomial probability P,

P(r Heads)=C(n,r)pr(1p)nr

Here,

p is the probability of heads,

C(n,r) is a binomial coefficient,

r is the number of successes in n tosses.

Calculation:

Use excel to draw a probability histogram for n=8 as shown in figure (1).

The probability histogram for n=8 is shown in figure (1), the number of heads that have the greatest probability of occurring is 4 and the number of heads that have the greatest probability of occurring are 50 for n=100

To determine

(b)

To draw:

The probability histogram for n=9 and find the number of heads that have the greatest probability of occurring for n=101.

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Chapter 14 Solutions

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