According to a recent survey of 1500 people, 64% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptablejob.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)O Part (a)In words, define the random variables X and P'.O Xis the number of people who feel the president is not doing an acceptable job, and P'is the proportion of people in the sample who feel the president is not doing an acceptable job.O Xis the proportion of people in the sample who feel the presidentsdoing an acceptable job, and P' is the number of people who feel the president is doing an acceptable job.O Xis the proportion of people in the sample who feel the president is not doing an acceptable job, and P'is the number of people who feel the president is not doing an acceptable job.O Xis the number of people who feel the presidentdoing an acceptable job, and P' is the proportionpeople in the sample who feel the president is doing an acceptable job.O Part (b)Which distribution should you use for this problem? (Round your answers to four decimal places.)P'-Explain your choice.O The standard normal distribution should be used because V npg z 10, which implies a large sample.O The standard normal distribution should be used because we are interested in proportions and the sample size is large.O The binomial distribution should be used because the two outcomes are "the president is doing a good job" and "the president is not doing a good job."O The Student's t-distribution should be used because we do not know the standard deviation. OPart (c)Constrlict a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job.(i) State the confidence interval. (Round your answers to four decimal places.)(ii) Sketch the graph.C.L. =%3DP'(iii) Calculate the error bound. (Round your answer to four decimal places.)8|N

According to a recent survey of 1500 people, 64% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptab job. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) In words, define the random variables X and P. O Xis the number of people who feel the president is not doing an acceptable job, and P'is the proportion of people in the sample who feel the president is not doing an acceptable job. O Xis the proportion of people in the sample who feel the president is doing an acceptable job, and Pis the number of people who feel the president is doing an acceptable job. O X is the proportion of people in the sample who feel the president is not doing an acceptable job, and P'is the number of people who feel the president is not doing an acceptable job. O Yis the pumber of people u

According to a recent survey of 1500 people, 64% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptab job. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) In words, define the random variables X and P. O Xis the number of people who feel the president is not doing an acceptable job, and P'is the proportion of people in the sample who feel the president is not doing an acceptable job. O Xis the proportion of people in the sample who feel the president is doing an acceptable job, and Pis the number of people who feel the president is doing an acceptable job. O X is the proportion of people in the sample who feel the president is not doing an acceptable job, and P'is the number of people who feel the president is not doing an acceptable job. O Yis the pumber of people u

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

According to a recent survey of 1500 people, 64% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable
job.
NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
O Part (a)
In words, define the random variables X and P'.
O Xis the number of people who feel the president is not doing an acceptable job, and P'is the proportion of people in the sample who feel the president is not doing an acceptable job.
O Xis the proportion of people in the sample who feel the president
sdoing an acceptable job, and P' is the number of people who feel the president is doing an acceptable job.
O Xis the proportion of people in the sample who feel the president is not doing an acceptable job, and P'is the number of people who feel the president is not doing an acceptable job.
O Xis the number of people who feel the president
doing an acceptable job, and P' is the proportion
people in the sample who feel the president is doing an acceptable job.
O Part (b)
Which distribution should you use for this problem? (Round your answers to four decimal places.)
P'-
Explain your choice.
O The standard normal distribution should be used because V npg z 10, which implies a large sample.
O The standard normal distribution should be used because we are interested in proportions and the sample size is large.
O The binomial distribution should be used because the two outcomes are "the president is doing a good job" and "the president is not doing a good job."
O The Student's t-distribution should be used because we do not know the standard deviation.

OPart (c)
Constrlict a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job.
(i) State the confidence interval. (Round your answers to four decimal places.)
(ii) Sketch the graph.
C.L. =
%3D
P'
(iii) Calculate the error bound. (Round your answer to four decimal places.)
8|N

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