Login Registrieren

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 6: Q. 102 (page 430)

Scrabble In the game of Scrabble, each player begins by drawing $7$ tiles from a bag containing $100$ tiles. There are $42$ vowels, $56$ consonants, and $2$ blank tiles in the bag. Cait chooses her $7$ tiles and is surprised to discover that all of them are vowels. Should we use a binomial distribution to approximate this probability? Justify your answer.

Short Answer

Expert verified

The probability could not be approximated using the binomial distribution.

Step by step solution

01

Given Information

The number of tiles chosen $= 7$

The number of vowels count $= 42$

The number of Consonant Count $= 56$

The total number of blank tiles $= 2$

02

According to question

The chances of success aren't predetermined in this case, and the trials are interdependent. Furthermore, for the binomial distribution, the probability of success for each trial must be specified. The trials must also be separate from one another.

As a result, the binomial distribution was unable to estimate the probability.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Ed and Adelaide attend the same high school but are in different math classes. The time E that it takes Ed to do his math homework follows a Normal distribution with mean 25 minutes and standard deviation 5 minutes. Adelaide's math homework time A follows a Normal distribution with mean 50 minutes and standard deviation 10 minutes. Assume that E and A are independent random variables.

a. Randomly select one math assignment of Ed's and one math assignment of Adelaide's. Let the random variable D be the difference in the amount of time each student spent on their assignments: $D = A - E$ . Find the mean and the standard deviation of D.

b. Find the probability that Ed spent longer on his assignment than Adelaide did on hers.

Victoria parks her car at the same garage every time she goes to work. Because she stays at work for different lengths of time each day, the fee the parking garage charges on a randomly selected day is a random variable, $G$ . The table gives the probability distribution of $G .$ You can check that $μ_{G} = \(14$ and $σ_{G} = \) 2.74$ .

In addition to the garage’s fee, the city charges a $$ 3$ use tax each time Victoria parks her car. Let $T =$ the total amount of money she pays on a randomly selected day.

a. Make a graph of the probability distribution of $T$ . Describe its shape.

b. Find and interpret $μ T$ .

c. Calculate and interpret $σ T$ .

Spoofing (4.2) To collect information such as passwords, online criminals use "spoofing" to direct Internet users to fraudulent websites. In one study of Internet fraud, students were warned about spoofing and then asked to log into their university account starting from the university's home page. In some cases, the log-in link led to the genuine dialog box. In others, the box looked genuine but, in fact, was linked to a different site that recorded the ID and password the student entered. The box that appeared for each student was determined at random. An alert student could detect the fraud by looking at the true Internet address displayed in the browser status bar, but most just entered their ID and password.

a. Is this an observational study or an experiment? Justify your answer.

b. What are the explanatory and response variables? Identify each variable as categorical or quantitative.

Benford’s law Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren’t present in legitimate records. Some patterns, like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford’s law. 4 Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit cannot be 0).

Part (a.) A histogram of the probability distribution is shown. Describe its shape.

Part (b). Calculate and interpret the expected value of X.

Time and motion A time-and-motion study measures the time required for an assembly-line worker to perform a repetitive task. The data show that the time required to bring a part from a bin to its position on an automobile chassis varies from car to car according to a Normal distribution with mean $11$ seconds and standard deviation $2$ seconds. The time required to attach the part to the chassis follows a Normal distribution with mean $20$ seconds and standard deviation $4$ seconds. The study finds that the times required for the two steps are independent. A part that takes a long time to position, for example, does not take more or less time to attach than other parts.

(a) Find the mean and standard deviation of the time required for the entire operation of positioning and attaching the part.

(b) Management’s goal is for the entire process to take less than $30$ seconds. Find the probability that this goal will be met. Show your work

See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

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.

Sign-up for free