/*! 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. 2.2 The probability distribution for... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

The probability distribution for the number of heads in four tosses of a coin is given by

Number of heads
01234
Probability
0.06250.2500
0.3750
0.2500
0.0625

The probability of getting at least one tail in four tosses of a coin is

a. 0.2500

b. 0.3125

c. 0.6875

d. 0.9375

e. 0.0625

Short Answer

Expert verified

(d) The probability of getting at least one tail in four tosses of a coin is 0.9375

Step by step solution

01

Given Information

The number of heads in four tosses of a coin is given by number of heads are 0,1,2,3,4

The probability are 0.0625 ,0.2500 , 0.3750, 0.2500 , 0.0625

02

Explanation for correct option

For the four coin tosses, they all have at least one tails event.

Implies that,

=P0+P1+P2+P30.0625+0.2500+0.3750+0.2500=0.9375

In four coin flips, the likelihood of receiving at least one tail is 0.9375

03

Explanation for incorrect option 

a. The probability of getting at least one tail in four tosses of a coin will not match with 0.2500

b. The probability of getting at least one tail in four tosses of a coin will not match with 0.3125

c. The probability of getting at least one tail in four tosses of a coin will not match with 0.6875

e. The probability of getting at least one tail in four tosses of a coin will not match with 0.0625

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 91Ó°ÊÓ!

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

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

c. in many samples, the values of the statistic are very close to the value of the

parameter.

d. in many samples, the values of the statistic are centered at the value of the parameter.

e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.

Dem bones (2.2) Osteoporosis is a condition in which the bones become brittle due to the loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in a standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD score that is 2.5standard deviations below the mean for young adults. BMD measurements in a population of people similar in age and gender roughly follow a Normal distribution.

a. What percent of healthy young adults have osteoporosis by the WHO criterion?

b. Women aged 70to 79are, of course, not young adults. The mean BMD in this age group is about-2 on the standard scale for young adults. Suppose that the standard deviation is the same as for young adults. What percent of this older population has osteoporosis?

The mean of this distribution (don’t try to find it) will be

a. very close to the median.

b. greater than the median.

c. less than the median.

d. You can’t say, because the distribution isn’t symmetric.

e. You can’t say, because the distribution isn’t Normal.

At a particular college, 78%of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100students and 72%of the respondents say they are receiving some sort of financial aid. Which of the following is true?

  1. 78%is a population and 72%is a sample.
  2. 72%is a population and 78%is a sample.
  3. 78%is a parameter and 72%is a statistic.
  4. 72%is a parameter and 78%is a statistic.
  5. 72%is a parameter and 100is a statistic.

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

a. reduce the bias of the estimate.

b. increase the bias of the estimate.

c. reduce the variability of the estimate.

d. increase the variability of the estimate.

e. reduce the bias and variability of the estimate.

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.