17) A study determined 35% of Millennials in America have no credit card debt. By assuming p = .35 is a success (nodebt), if a random sample of 50 millennials was selected, find the probability that 20 of them have no debt. Use thenormal distribution as an approximation to solve this binomial problem.To help explain why it is appropriate we can do this, indicate the appropriate variables for a normal approximationto a binomial distribution, and the proper inequality statements.Number of trials: nNumber of successes: Probability of Success: pProbability of Failure: qnp > 5 and ng> 5O Number of trials: Number of successes: nProbability of Success: pProbability of Failure: gnp > 5 and ng> 5O Number of trials: nNumber of successes: Probability of Success: qProbability of Failure: pnp > 5 and ng > 5O Number of trials: n Number of successes: Probability of Success: pProbability of Failure: anp< 5 and ng< 5

Answered: Image /qna-images/answer/7463c1e1-3141-4c81-988f-dcbb77c7983b.jpg

Answered: 17) A study determined 35% of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a recent election 66% of people supported reelecting the incumbent. Suppose a poll is done of 1470 people. If we used the normal as an approximation to the binomial, what would the mean and standard deviation be?
A random variable Xis binomially distributed with mean 4 and standard deviation 2.4. Find the probability that more than half the trials are successes.
A random variable has a longnormal distribution with mean 10 and variance 4. Calculate the probability that the variable will take a value between 7.5 and 12.5
4 Thirty five percent of the students in a class of 100 are planning to go to graduate school, Find the variance of this binomial distribution
A Binomial experiment has 100 trials and a probability of success of 0.8.Determine the mean of this experiment.
Based on long experience, an airline found that about 8% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 265 ticket reservations for an airplane with only 255 seats. (a) What is the probability that a person holding a reservation will show up for the flight? (c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)
According to a recent Gallup poll, about 5% of Americans polled say they are vegetarian (abstaining from eating meat). This number has not changed since the poll done in 2012. If I ask a random group of 750 Americans if they vegetarian or not, what is the chance that 45 or more will say that they are vegetarian? 1. Use the binomial distribution on Geogebra (or your calculator) to solve this problem, show your work on paper (what you are putting into technology) 2. Use the normal approximation to the binomial to solve this same problem. Show your work on paper (what you are putting into technology)
The average life of a certain battery is 7 years, with a standardeviation of 2 year. A random sample of size 16 of such batteries Assume that the live of the battery approximately follows a normal distribution. What is the probability that the average life will be at most 8 years?
According to the Current Population Survey (Internet Release date: September 2004), 42% of females between the ages of 18 and 24 years lived at home in 2003. (Unmarried college students living in a dorm are counted as living at home). Suppose a survey is administered today to 425 randomly selected females between the age of 18 and 24 years and 204 respond that they live at home. 1. Does this define a binomial distribution? Justify your answer 2. If so, can you use the normal approximation to binomial distribution? Justify your answer and state what the mean and standard deviation of the normal approximation are. 3. Using the binomial probability distribution, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42%? 4. Using the normal approximation to binomial, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42%?
Last year, a person wrote 118 checks. Let the random variable x represent the number of checks he wrote in one day, and assume that it has a Poisson distribution. What is the mean number of checks written per day? What is the standard deviation? What is the variance?
In studies for a medication, 12 percent of patients gained weight as a side effect. Suppose 530 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 64 patients will gain weight as a side effect. (b) no more than 64 patients will gain weight as a side effect. (c) at least 75 patients will gain weight as a side effect. What does this result suggest?
Suppose that the fraction of defective modems shipped by a data-communications vendor has an approximation beta distribution with a=5 and b=21. find the mean and variance of the fraction of defective modems per shipment What is the probability that a randomly selected shipment will contain at least 30 % defectives? What is the probability that a randomly selected shipment will contain no more than 5 % defectives?

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