/*! 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} Q. 83 83. Random digit dialing Refer t... [FREE SOLUTION] | 91影视

91影视

83. Random digit dialing Refer to Exercise 81. Let Y= the number of calls that don鈥檛 reach a live person.

(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
(b) Find the standard deviation of Y.How is it related to the standard deviation of X? Explain why this makes sense

Short Answer

Expert verified

(a) The mean of Yis Y=15-X=12

(b) The standard deviation of Y is Y=X1.5492

Step by step solution

01

Part (a) Step 1: Given information 

Let Y=the number of calls that don鈥檛 reach a live person.

02

Part (a) Step 2: Explanation

Given: n=15, and p=0.20

Since, Yis equal to X, and the only difference is that the terms "success" and "failure" have been swapped.

The mean for the sample size nand the probabilityp is:
pY=1-pX=1-0.20=0.80
Here, n=15
Y=np=15(0.80)=12

Since, the mean of Yis the sample size ndropped by the mean of X.

03

Part (b) Step 1: Given explanation 

The standard deviation ofYis related to the standard deviation of X.

04

Part (b) Step 2: Explanation 

Given: n=15, and p=0.20

Since, Yis equal to X, and the only distinction is that the terms "success" and "failure" have been swapped.

The standard deviation for the sample size n, and the probability pis,

pY=1-pX=1-0.20=0.80
Here,n=15
Y=(np)(1-p)=15(0.80)(1-0.80)=1.5492

Since, the standard deviation for Xand Yare similar.

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

Rotter Partners is planning a major investment. The amount of profit X(in millions of dollars) is uncertain, but an estimate gives the following probability distribution:

Based on this estimate, X=3and X=2.52

Rotter Partners owes its lender a fee of $200,000plus 10%of the profits X. So the firm actually retains Y=0.9X-0.2from the investment. Find the mean and standard deviation of the amount Ythat the firm actually retains from the investment.

A machine fastens plastic screwon caps onto containers of motor oil. If the machine applies more torque than the cap can withstand, the cap will break. Both the torque applied and the strength of the caps vary. The capping-machine torqueTfollows a Normal distribution with mean 7inch-pounds and standard deviation 0.9inch-pounds. The cap strength C (the torque that would break the cap) follows a Normal distribution with mean 10 inch-pounds and standard deviation1.2 inch-pounds.

(a) Explain why it is reasonable to assume that the cap strength and the torque applied by the machine are independent.

(b) Let the random variableD=CT. Find its mean and standard deviation.

(c) What is the probability that a cap will break while being fastened by the machine? Show your work.

85. Aircraft engines Engineers define reliability as the probability that an item will perform its function under specific conditions for a specific period of time. A certain model of aircraft engine is designed so that each engine has probability 0.999 of performing properly for an hour of flight. Company engineers test an SRS of 350 engines of this model. Let X= the number that operate for an hour without failure.
(a) Explain whyX is a binomial random variable.

(b) Find the mean and standard deviation ofX. Interpret each value in context.
(c) Two engines failed the test. Are you convinced that this model of engine is less reliable than it鈥檚 supposed to be? Compute P(X348) and use the result to justify your answer.

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

顿别铿乶别 =+

The dealership鈥檚 manager receives a 500bonus for each car sold and a 300 bonus for each car leased. Find the mean and standard deviation of the manager鈥檚 total bonus B. Show your work.

Keno is a favorite game in casinos, and similar games are popular in the states that operate lotteries. Balls numbered 1to 80are tumbled in a machine as the bets are placed, then 20of the balls are chosen at random. Players select numbers by marking a card. The simplest of the many wagers available is 鈥淢ark 1Number.鈥 Your payoff is 3on a bet if the number you select is one of those chosen. Because 20of 80numbers are chosen, your probability of winning is 20/80, or 0.25. Let X=the amount you gain on a single play of the game.

(a) Make a table that shows the probability distribution of X.

(b) Compute the expected value of X. Explain what this result means for the player

See all solutions

Recommended explanations on Math Textbooks

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.