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Unformatted text preview: Answers: a M W,
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March 14, 2011 1) The records at El, Inc. indicate that 65% of the firm’s employees have
completed a client relations training program. A simple random
sample of 400 employees was taken from this population for further
study. a. What is the probability that the sample proportion p will bewﬂw £31 between 0.75 and 0.55? x” f M WWW/«r ‘“ (if hm ' W l l ’ / l? > ./’ g MW (“'"M‘WWTT, 1
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that the sample proportion p wi 1 be between 0.70 and 0.60?
a? \m \R What is the prohahility that the sample proPOrtion F Will be between 0.70 and 0.60? // E “i not w a» a i, 7,
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\. 2) A political pollster is conducting a poll in order to make predictions
on election night. Assuming a twocandidate election, if a speciﬁc
candidate receives 58% or more of the vote in the sample, then that
candidate will be forecast as the Winner of the election. If a random
sample of 100 voters is selected: a. What is the probability that a candidate will be forecast the winner
if the true percentage of the vote for that candidate is 48% (and
that candidate will actually 1 e the election)? """”'W”"‘”" MK . i 4 W» m w "1 ’g ' 3%“ MM 6 {a //,,w ) {It if EEK” Ww':‘:;
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b. What is the probability that a candidate Will NOT be forecast the
winner if the true percentage of the vote for that candidate is 53%
(and that candidate will actually win the election)? 1. Some “Rules of Thumb” for the Problems in this Quiz In the types of problems on the front page, if you get a zuscore off the table
(i.e. > 3.09) the probability will always be > 2 X .499 or > .998. For the problem on the back page, here are some hints: a.) The “cut off point” is the percentage (proportion) in the sample speciﬁed
as the point at which the pollster will call the candidate a winner if the
percentage in the sample that said they voted for that candidate was
greater than or equal to that percentage speciﬁed. b.) The next step requires the determination of the sampling distribution,
which and is centered on the ACTUAL percentage of votes that candidate
received and requires the calculation of the standard error of the
proportion. c.) The portion of the curve to the RIGHT of the “cut off point” represents
the probability the pollster will forecast the candidate a winner. d.) The portion of the curve to the LEFT of the “cut off point” represents the
probability the pollster will NOT forecast the candidate a winner. e.) If the “cut off point” is to the RIGHT of the center of the curve, which is set at the ACTUAL proportion of votes that candidate received, then determine the zscore, go to the table and do the following “1  (.5 + the
number from the table) If the “cut off point” is to the LEFT of the center of the curve, which is set at the ACTUAL proportion of votes that candidate received, then determine the zscore, go to the table and do the following “ (.5 + the
number from the table) f.) ...
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 Summer '08
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