Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q.69 (page 403)

Explain whether the given random variable has a binomial distribution Sowing seeds Seed Depot advertises that 85%of its flower seeds will germinate (grow). Suppose that the company’s claim is true. Judy buys a packet with 20flower seeds from Seed Depot and plants them in her garden. Let X=the number of seeds that germinate

Short Answer

Expert verified

The distribution is binomial if the independence of events holds

Step by step solution

01

Given Information

Given that sowing seeds, Seed Depot advertises that 85%of its flower seeds will germinate (grow).

Judy buys a packet with 20flower seeds from Seed Depot and plants them in her garden

02

Explanation

If each succeeding draw is independent of the previous draw, the variable X is said to have a binomial distribution in the given question. In this example, success means that the seed germinates and a fixed number of 20 seeds are drawn, with an 85 percent chance of success.

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

Blood types In the United States, 44%of adults have type O blood. Suppose we choose 7U.S. adults at random. Let X=the number who have type O blood. Use the binomial probability formula to find P(X=4). Interpret this result in context.

45. Too cool at the cabin? During the winter months, the temperatures at the Stameses' Colorado cabin can stay well below freezing 32°For 0°Cfor weeks at a time. To prevent the pipes from freezing, Mrs. Stames sets the thermostat at 50°F. She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years' worth of data, the temperature Tin the cabin at midnight on a randomly selected night follows a Normal distribution with mean 8.5°Cand standard deviation2.25°C.
(a) Let Y=the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that F=(9/5)C+32). Find the mean and standard deviation of Y.

(b) Find the probability that the midnight temperature in the cabin is below 40°F. Show your work.

46. Cereal A company's single-serving cereal boxes advertise 9.63 ounces of cereal. In fact, the amount of cereal X in a randomly selected box follows a Normal distribution with a mean of 9.70 ounces and a standard deviation of 0.03 ounces.
(a) LetY=the excess amount of cereal beyond what's advertised in a randomly selected box, measured in grams ( 1 ounce =28.35grams). Find the mean and standard deviation of Y.
(b) Find the probability of getting at least 3 grams more cereal than advertised.

Lie detectors A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of suggesting that the person is deceptive. A company asks 12job applicants about thefts from
previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X=the number of people who the lie detector says are being deceptive.
(a) Find and interpret μX.
(b) Find and interpret σX.

50. Checking independence For each of the following situations, would you expect the random variables Xand Yto be independent? Explain your answers.

(a)Xis the rainfall (in inches) on November 6of this year, and Yis the rainfall at the same location on November 6 of next year.
(b) Xis the amount of rainfall today, and Y is the rainfall at the same location tomorrow.
(c) Xis today's rainfall at the airport in Orlando, Florida, and Y is today's rainfall at Disney World just outside Orlando.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Decision 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.

Sign-up for free