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Chapter 15: Q14MP (page 777)

Suppose a200 -page book has, on the average, one misprint every 10 pages. On about how many pages would you expect to find2misprints?

Short Answer

Expert verified

The number of pages is . $N_{p} = 1$

Step by step solution

01

Given Information

A 200 page book has, on the average, one misprint every10 pages.

02

Definition of the Poisson distribution.

A discrete frequency distribution that indicates the likelihood of a set of independent occurrences occurring at a specific moment.

03

Find the number of pages.

The formula for Poisson distribution states that. $P_{n} = \frac{μ^{n} e^{- μ}}{n!}$

The average is given below.

$μ = 0.1$

Probabilities are given below.

$\begin{matrix} P_{n} = \frac{{(0.1)}^{n} e^{- 0.1}}{n!} \\ P_{2} = \frac{{(0.1)}^{2} e^{- 0.1}}{2!} \\ = 0.0045 \end{matrix}$

The number of the pages is given below.

$\begin{matrix} N_{p} = N \times P_{2} \\ = 0.0045 \times 200 \\ \approx 1 \end{matrix}$

The number of pages is . $N_{p} = 1$

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Most popular questions from this chapter

A bank allows one person to have only one savings account insured to $100,000.However, a larger family may have accounts for each individual, and also accountingthe names of any 2 people, any 3 and so on. How many accounts are possible for afamily of 2? Of 3? Of 5? Of? Hint: See Problem 2.

Define s by the equation. $s^{2} = (1 / n) \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}$ Show that the expected valueof. $s^{2} is [(n - 1) / n] σ^{2}$ Hints: Write

$\begin{matrix} {(x_{i} - \bar{x})}^{2} = {[(x_{i} - μ) - (\bar{x} - μ)]}^{2} \\ = {(x_{i} - μ)}^{2} - 2 (x_{i} - μ) {(\bar{x} - μ) + \bar{(x} - μ)}^{2} \end{matrix}$

Find the average value of the first term from the definition of $σ^{2}$ and the average value of the third term from Problem 2. To find the average value of the middle term write

$\begin{matrix} (\bar{x} - μ) = (\frac{x_{1} + x_{2} + \dots + x_{n}}{n} - μ) \\ = \frac{1}{n} [(x_{1} - μ) + (x_{2} - μ) + \dots + (x_{n} - μ)] \end{matrix}$

Show by Problemthat

$\begin{matrix} E [(x_{i} - μ) (x_{j} - μ)] = E (x_{i} - μ) E (x_{j} - μ) \\ = 0 for i \neq j \end{matrix}$

andevaluate $6 .14$ (same as the first term). Collect terms to find

$E (s^{2}) = \frac{n - 1}{n} σ^{2}$

Three coins are tossed; x = number of heads minus number of tails.

A true coin is tossed 104 times.

(a) Find the probability of getting exactly 5000 heads.

(b) Find the probability of between4900and 5075 heads.

What is the probability that the 2 and 3 of clubs are next to each other in a shuffled deck? Hint: Imagine the two cards accidentally stuck together and shuffled as one card.

See all solutions

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