/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q1BSC Notation In analyzing hits by V-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q1BSC (page 184)

Notation In analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 \(k{m^2}\) . A total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying Formula 5-9, identify the values of \(\mu \), x, and e. Also, briefly describe what each of those symbols represents.

Short Answer

Expert verified

\(\mu \)denotes the mean number of bomb hits per region. Its value is equal to 0.929.

x denotes the number of hits required to compute the desired probability. Its value is equal to 2.

e denotes the constant in the Poisson probability formula. Its value is approximately equal to 2.71828.

Step by step solution

01

Given information

It is given that a total of 535 bomb hits the area of South London with 576 regions.

02

Identify the values and the meaning of symbols\(\mu \), x, and e

The mean number of hits per region is denoted by\(\mu \).

The value of\(\mu \)is computed below:

\(\begin{array}{c}\mu = \frac{{{\rm{Number}}\;{\rm{of}}\;{\rm{bomb}}\;{\rm{hits}}}}{{{\rm{Number}}\;{\rm{of}}\;{\rm{regions}}}}\\ = \frac{{535}}{{576}}\\ = 0.929\end{array}\)

Thus,\(\mu = 0.929\).

The number of hits required to compute the probability is denoted by x.

Here, x=2.

e is the constant that is used in the Poisson probability formula. It is also called the Euler鈥檚 number.

The value of e is approximately equal to 2.71828.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises 7鈥�14, determine whether a probability

distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.

When betting on the pass line in the dice game of craps at the Mohegan Sun casino in Connecticut, the table lists the probabilities for the number of bets that must be placed in order to have a win.

x

P(x)

1

0.493

2

0.25

3

0.127

4

0.064

There are 80 questions from an SAT test, and they are allmultiple choice with possible answersof a, b, c, d, e. For each question, only one answer is correct. Find the mean and standarddeviation for the numbers of correct answers for those who make random guesses for all 80

questions.

Expected Value in Virginia鈥檚 Pick 3 Game In Virginia鈥檚 Pick 3 lottery game, you can pay \(1 to select a three-digit number from 000 through 999. If you select the same sequence of three digits that are drawn, you win and collect \)500.

a. How many different selections are possible?

b. What is the probability of winning?

c. If you win, what is your net profit?

d. Find the expected value.

e. If you bet \(1 in Virginia鈥檚 Pick 4 game, the expected value is -50垄. Which bet is better in the sense of a producing a higher expected value: A \)1 bet in the Virginia Pick 3 game or a $1 bet in the Virginia Pick 4 game?

Detecting FraudThe Brooklyn District Attorney鈥檚 office analyzed the leading (leftmost) digits of check amounts in order to identify fraud. The leading digit of 1 is expected to occur 30.1% of the time, according to 鈥淏enford鈥檚 law,鈥� which applies in this case. Among 784 checks issued by a suspect company, there were none with amounts that had a leading digit of 1.

a. If there is a 30.1% chance that the leading digit of the check amount is 1, what is the expected number of checks among 784 that should have a leading digit of 1?

b. Assume that groups of 784 checks are randomly selected. Find the mean and standard deviation for the numbers of checks with amounts having a leading digit of 1.

c. Use the results from part (b) and the range rule of thumb to identify the values that are significantly low.

d. Given that the 784 actual check amounts had no leading digits of 1, is there very strong evidence that the suspect checks are very different from the expected results? Why or why not?

Expected Value for the Ohio Pick 4 Lottery In the Ohio Pick 4 lottery, you can bet \(1 by selecting four digits, each between 0 and 9 inclusive. If the same four numbers are drawn in the same order, you win and collect \)5000.

a. How many different selections are possible?

b. What is the probability of winning?

c. If you win, what is your net profit?

d. Find the expected value for a \(1 bet.

e. If you bet \)1 on the pass line in the casino dice game of craps, the expected value is -1.4垄. Which bet is better in the sense of producing a higher expected value: a \(1 bet in the Ohio Pick 4 lottery or a \)1 bet on the pass line in craps?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.