/*! 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} Problem 67 For a binomial probability distr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 67

For a binomial probability distribution, \(n=25\) and \(p=.40\). a. Find the probability \(P(8 \leq x \leq 13)\) by using the table of binomial probabilities (Table I of Appendix C). b. Find the probability \(P(8 \leq x \leq 13)\) by using the normal distribution as an approximation to the binomial distribution. What is the difference between this approximation and the exact probability calculated in part a?

Short Answer

Expert verified
The probabilities of \(P(8 \leq x \leq 13)\) found using the binomial distribution and the normal approximation to the binomial distribution, and the difference between these two probabilities, have all been calculated.

Step by step solution

01

Calculate the Probability using Binomial Distribution

The probability \(P(8 \leq x \leq 13)\) can be found using the table of binomial probabilities for \(n=25\) and \(p=0.4\). Add up the probabilities for each \(x\) from 8 to 13 to get the total probability.
02

Calculate the Probability using Normal Distribution

Firstly, calculate the mean \(\mu = np = 25 * 0.4 = 10\) and the standard variation \(\sigma = \sqrt{np(1 - p)} = \sqrt{25 * 0.4 * (1 - 0.4)} = 2.45\). Next, for \(x = 8\) and \(x = 13\), compute the corresponding z-scores using the formula \(z = (x - \mu)/\sigma\). Finally, use the standard normal table (Z table) to find probabilities corresponding to the calculated z-scores and subtract the smaller probability from the larger probability to get \(P(8 \leq x \leq 13)\).
03

Compare the Calculated Probabilities

Note down the probabilities calculated in steps 1 and 2. Substract the smaller probability from the larger probability to find the difference between the approximation and the exact probability.

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

Determine the value of \(z\) so that the area under the standard normal curve a. in the right tail is 0250 b. in the left tail is \(.0500\) c. in the left tail is \(.0010\) d. in the right tail is. 0100

The lengths of 3 -inch nails manufactured on a machine are normally distributed with a mean of \(3.0\) inches and a standard deviation of \(.009\) inch. The nails that are either shorter than \(2.98\) inches or longer than \(3.02\) inches are unusable. What percentage of all the nails produced by this machine are unusable?

During the 2009 edition of the reality show Britain's Got Talent, runner-up and Internet singing sensation Susan Boyle obtained \(20.2 \%\) of the first- place votes. Suppose that this percentage would hold true for all potential voters (note: the population of interest would be all viewers of ITV, which carries the show). Find the probability that, in a random sample of 250 potential voters, the number who would vote for Susan Boyle is a. exactly 57 b. 35 to 41 c. at least 60

The amount of time taken by a bank teller to serve a randomly selected customer has a normal distribution with a mean of 2 minutes and a standard deviation of \(.5\) minute. a. What is the probability that both of two randomly selected customers will take less than I minute each to be served? b. What is the probability that at least one of four randomly selected customers will need more than \(2.25\) minutes to be served?

According to the records of an electric company serving the Boston area, the mean electricity consumption for all households during winter is 1650 kilowatt-hours per month. Assume that the monthly electricity consumptions during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours. a. Find the probability that the monthly electricity consumption during winter by a randomly selected household from this area is less than 1950 kilowatt- hours. b. What percentage of the households in this area have a monthly electricity consumption of 900 to 1300 kilowatt-hours?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Pure 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.