Ordering ProbabilitiesDate: 08/16/97 at 12:34:49 From: Amy Hunter Subject: Statistics In a restaurant, the proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of the restaurant is taken. What is the expected value, standard deviation, and shape of the sampling distribution of p? What is the probability that the proportion of people who will order coffee with their meal is between .85 and .875? What is the probability that the proportion of people who will order coffee with their meal is at least .945? I don't understand the proportions and probabilities. Thanks. Date: 08/16/97 at 17:14:34 From: Doctor Anthony Subject: Re: Statistics >What is the expected value, standard deviation, and shape of the sampling distribution of p? This is a binomial probability with mean = np = 144 x 0.9 = 129.6 variance = npq = 144 x .9 x .1 = 12.96 s.d = sqrt(12.96) = 3.6 If dealing with proportions of successes, mean = p = 0.9 variance = pq/n = .9 x .1/144 = .000625 s.d = sqrt(pq/n) = .025 >What is the probability that the proportion of people who will order coffee with their meal is between .85 and .875? .85 - .9 z1 = ---------- = - 2.0 A(z1) = .9772 .025 .875 - .9 z2 = ----------- = - 1.0 A(z2) = .8413 .025 The area we require is that between z1 and z2 = .9772 - .8413 = 0.1359 So the probability that the proportion is between .85 and .875 is 0.1359. >What is the probability that the proportion of people who will order coffee with their meal is at least .945? .945 - .9 z = --------- = 1.8 A(z) = 0.9641 .025 The probability that the proportion is .945 or greater is 1 - .9641 = .0359 -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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