/*! 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} Q14E A contractor is required by a co... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q14E (page 107)

A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature of the project) in applying for a building permit. Let Y = the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y鈥攖hat is,\(p\left( y \right) = ky\)for\(y = 1, \ldots ,5\).

a. What is the value of k? (Hint:\(\sum\limits_{y = 1}^5 {p\left( y \right)} = 1\))

b. What is the probability that at most three forms arerequired?

c. What is the probability that between two and fourforms (inclusive) are required?

d. Could \(p\left( y \right) = \frac{{{y^2}}}{{50}}\)for \(y = 1, \ldots ,5\)be the pmf of Y?

Short Answer

Expert verified

a. The value of k is\(\frac{1}{{15}}\).

b.The probability that at most three forms are required is0.4.

c.The probability that between two and four forms (inclusive) are required is0.6.

d. No, p(y) is not a pmf of y.

Step by step solution

01

Step 1

It is given that,the probability that y forms are required is known to be proportional to y is\(p\left( y \right) = ky\,\,\,{\rm{for}}\,y = 1,2,3, \ldots ,5\). The total number of forms in applying the building submit is 5.

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

Of the people passing through an airport metal detector, .5% activate it; let \(X = \) the number among a randomly selected group of 500 who activate the detector.

a. What is the (approximate) pmf of X?

b. Compute \({\bf{P}}(X = 5)\)

c. Compute \({\bf{P}}(5 \le X)\)

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices, with P(A)\({\rm{ = }}{\rm{.5}}\), P(B)\({\rm{ = }}{\rm{.2}}\), and P(C)\({\rm{ = }}{\rm{.3}}\). a. Among the next\({\rm{100}}\)customers, what are the mean and variance of the number who pay with a debit card? Explain your reasoning. b. Answer part (a) for the number among the\({\rm{100}}\)who don鈥檛 pay with cash.

A newsstand has ordered five copies of a certain issue of a photography magazine. Let \({\rm{X = }}\)the number of individuals who come in to purchase this magazine. If \({\rm{X}}\) has a Poisson distribution with parameter \({\rm{\mu = 4}}\), what is the expected number of copies that are sold?

A plan for an executive travellers鈥� club has been developed by an airline on the premise that \({\rm{10\% }}\) of its current customers would qualify for membership.

a. Assuming the validity of this premise, among \({\rm{25}}\) randomly selected current customers, what is the probability that between \({\rm{2}}\) and \({\rm{6}}\) (inclusive) qualify for membership?

b. Again assuming the validity of the premise, what are the expected number of customers who qualify and the standard deviation of the number who qualify in a random sample of \({\rm{100}}\) current customers?

c. Let \({\rm{X}}\) denote the number in a random sample of \({\rm{25}}\) current customers who qualify for membership. Consider rejecting the company鈥檚 premise in favour of the claim that \({\rm{p > 10}}\) if \({\rm{x}} \ge {\rm{7}}\). What is the probability that the company鈥檚 premise is rejected when it is actually valid?

d. Refer to the decision rule introduced in part (c). What is the probability that the company鈥檚 premise is not rejected even though \({\rm{p = }}{\rm{.20}}\) (i.e., \({\rm{20\% }}\) qualify)?

Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a \({\rm{\alpha = 2}}\) per square yard. How large should the radius \({\rm{R}}\) of a circular sampling region be taken so that the probability of finding at least one in the region equals \({\rm{.99}}\)?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Mechanics 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.