only need d,e,f,g What proportion of NY Monopoly scratch-off Lotto tickets are winners? We will examine this by taking a random sample of n = 4178 Monopoly scratch-offs. Of these, x = 912 were winners. Let p be the (unknown) trueproportion of NY Monopoly scratch offs which are winners. We want to estimate p. X is the random variable representing the number of sampled Monopoly scratch-offs which are winners.a) What type of probability distribution does X have?O PoissonO WeibullC gammaO exponentialO binomialb) What was the sample proportion, p, of sampled Monopoly scratch offs which were winners?c) What is the R formula for the expected value of X in terms of n and p?O n*pO n^2O n*p*(1 - p)O sqrt(n*p*(1-p))O 1/pd) What is the z critical value that we would use to construct a classical 95% confidence interval for p?e) Construct a 95% classical confidence interval for p? (f) How long is the 95% classical confidence interval for p?g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval?h) Copy your R script for the above into the text box here.

Given Information: The sample size, n=4178 The number of Monopoly scratch-off winners, x=912

d) What is the z critical value that we would use to construct a classical 95% confidence interval for p? e) Construct a 95% classical confidence interval for p? ([ f) How long is the 95% classical confidence interval for p? g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval?

d) What is the z critical value that we would use to construct a classical 95% confidence interval for p? e) Construct a 95% classical confidence interval for p? ([ f) How long is the 95% classical confidence interval for p? g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

only need d,e,f,g

What proportion of NY Monopoly scratch-off Lotto tickets are winners? We will examine this by taking a random sample of n = 4178 Monopoly scratch-offs. Of these, x = 912 were winners. Let p be the (unknown) true
proportion of NY Monopoly scratch offs which are winners. We want to estimate p. X is the random variable representing the number of sampled Monopoly scratch-offs which are winners.
a) What type of probability distribution does X have?
O Poisson
O Weibull
C gamma
O exponential
O binomial
b) What was the sample proportion, p, of sampled Monopoly scratch offs which were winners?
c) What is the R formula for the expected value of X in terms of n and p?
O n*p
O n^2
O n*p*(1 - p)
O sqrt(n*p*(1-p))
O 1/p
d) What is the z critical value that we would use to construct a classical 95% confidence interval for p?
e) Construct a 95% classical confidence interval for p? (
f) How long is the 95% classical confidence interval for p?
g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval?
h) Copy your R script for the above into the text box here.

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