Question 433383: In a local university, 40% of the students live in dormitories. A random sample of n = 80 students is selected for a particular study.
(a) What is the sampling distribution of P? Please provide its general shape, its standard deviation, and its mean.
(b) What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a local university, 40% of the students live in dormitories. A random sample of n = 80 students is selected for a particular study.
(a) What is the sampling distribution of P?
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Note: You have not provided a description of P.
Is it the proportions of all samples of size 80?
Is it the
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If it is the population:
mean = np = 80*0.4 = 32
std = sqrt(npq) = sqrt(32*0.6) = 4.3817..
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If it is the proportions of samples of size 80:
mean = 0.4
std = sqrt[0.4*0.6/80] = 0.0548
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Please provide its general shape, its standard deviation, and its mean.
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(b) What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50?
z(0.3) = (0.3-0.4)/0.0549 = -1.8215
z(0.5) = (0.5-0.4)/0.0549 = 1.8215
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P(0.3< x <0.5) = (-1.8215< x < 1.8215) = 0.9315
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Cheers,
Stan H.
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