Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

Q. 102

Expert-verified
Introductory Statistics
Found in: Page 295
Introductory Statistics

Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 people in Uganda. Let X = the number of people who have access to electricity.

a. What is the probability distribution for X?

b. Using the formulas, calculate the mean and standard deviation of X.

c. Use your calculator to find the probability that 15 people in the sample have access to electricity.

d. Find the probability that at most ten people in the sample have access to electricity.

e. Find the probability that more than 25 people in the sample have access to electricity

a. The probability distribution of X is 0.09

b. The mean is 13.5 and standard deviation is 3.5

c. The probability that 15 people in the sample have access to electricity is 0.0988

d. The probability that at most ten people in the sample have access to electricity is 0.1987

e. The probability that more than 25 people in the sample have access to electricity is 0.9991

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Content Introduction

The binomial distribution determines the probability of looking at a specific quantity of a hit results in a specific quantity of trials

Step 2: Explanation (part a)

We are given,

9% of the population of Uganda had access to electricity as of 2009 and we randomly chose a sample of 150 people in Uganda. So. here n is the sample size and p is the probability.

Therefore,

The probability distribution of X is p=0.09

Step 2: Explanation (part b)

We are given: n=150, p=0.09

The mean is:

μ=np, where

n= number of samples p=probability of samples

Therefore, the mean is

role="math" localid="1649250625500" μ=npμ=150×0.09μ=13.5

Standard deviation is:

σ=np(1-p)σ=150×0.09 (1-0.09)σ=3.5

Step 4: Explanation (part c)

Using binompdf:

the probability that 15 people in the sample have access to electricity is:

role="math" localid="1649250800761" binompdf (150, 0.09, 15)=150!15! (150-15)!0.0915(1-0.09)50-15 binompdf (150, 0.09, 15)=150!15! (150-15)!0.0915(1-0.09)35binompdf (150, 0.09, 15)=0.0988

Step 5: Explanation (part d) 

The probability that at most ten people in the sample have access to electricity is:

binompdf (150, 0.09, 10)=∑k=010150!! (k150-k)!0.09k(1-0.09)50-kbinompdf (150, 0.09, 10)=0.1897

Step 6: Explanation (part e)

The probability that more than 25 people in the sample have access to electricity is:

binompdf (150, 0.09, 25)=∑k=025150!! (k150-k)!0.09k(1-0.09)50-kbinompdf (150, 0.09, 25)=0.9991

Most popular questions for Math Textbooks

The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in Afghanistan is 12%. Let X = the number of Afghani women you ask until one says that she is literate.

a. What is the probability distribution of X?

b. What is the probability that you ask five women before one says she is literate?

c. What is the probability that you must ask ten women?

d. Find the (i) mean and (ii) standard deviation of X.

A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. Let X = the number of times a patient rings the nurse during a 12-hour shift. For this exercise, x = 0, 1, 2, 3, 4, 5. P(x) = the probability that X takes on value x. Why is this a discrete probability distribution function (two reasons)?

What does the column “P(x)” sum to?

Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to

sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established

a probability distribution.

Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number who participated in after-school sports all four years of high school.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many seniors are expected to have participated in after-school sports all four years of high school?

e. Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.

f. Based upon numerical values, is it more likely that four or that five of the seniors participated in after-school sports all four years of high school? Justify your answer numerically

Use the following information to answer the next six exercises: On average, a clothing store gets 120 customers per day.

What is the probability of getting 35 customers in the first four hours? Assume the store is open 12 hours each day.
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Math Textbooks

Decision Maths

Read explanation

Probability and Statistics

Read explanation

Statistics

Read explanation

Mechanics Maths

Read explanation

Geometry

Read explanation

Calculus

Read explanation

Pure Maths

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.