Please help with Statisticts! Thank you! A poll of 500 randomly registered voter

Question

Please help with Statisticts! Thank you!

A poll of 500 randomly registered voters was recently administered. Respondents were asked, "Do you aprove of President Bush's policies relating to the war in Iraq" Suppose that we know that 40% of all registered voters approve of the polocies.

a) What is the random variable X?

b) Is X bimomial? Suport your answer.

c) What is the probability that a most 185 voters responded yes to the question?

d) how many voters would you expect to respond yes?

2.Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. A bank conducts interview of job applicants with the use of the lie detector. There are 15 applicants who were interwiewed.

a) assu,ing all 15 applicants tell the truth, what is the probability that the lie doctor will conclude that all 15 are telling the truth?

b) Assuming all 15 applicants tell the truth, what is the probability that lie doctor will conclude that as least one is lying.

c) That are the mean and standard deviation of the 15 applicants the lie doctor concludes are lying?

d) What is the probability that the number of truthful applicants classified as liars is greater that the mean?

3. DHL Shipping claims that it ships 95% of its orders within the three working days. You select a simple random sample of 100 orders were shipped on time.

a) If DHL realy does ship 95% of its orders on time, what is the probability that the the company shiped 91 or fewer out of 100 orders were shipped on time?

b) A market from UPS jumps on the research stating, They claim 95% on time, but by their own research they ship only 91% on time. Provide a rebuttal to the UPS markerter in nonstatistical terms.

Explanation / Answer

answer

1)a. # from sample who responded "yes"

b. yes/no case, fixed # of trials, independence , p constant

c. using a binomial calculator, P[x 185] = .9219

2)a)
n=15 (number of applicants)
p=.85 probability that the lie detector will conclude that a person is telling the truth.
x= 15 (out of 15 how many)

This is binomial probability
P(x=k)=nCk p^k (1-p)^(n-k)
P(x=15) = 15C15 (.85)^15 (.15)^0 = (0.85)^15 = 0.08735

b)
probability of false detection = .15
n=15
p=.15
x = at least 1
P( at least 1 lying) = 1-P(no one lying) 1- 15C0 (.15)^0 (.85)^15
= 1-(0.85)^15 =1-0.08735 = 0.91285

c)
mean = np = 15(.85)= 12.75
standard deviation = sqrt[15(.85)(.15)] = 1.3829

d)
number of truthful applicants classified as liars = 15(.15) =2.25
P(2.25 > 12.75) = 0.0

3)

qa
x is bin(100,0.95)
P(x 91) = 6.31% <-----

qb
95% is a sort of average
P(91 or more) is as high as 97.2%

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