Reference no: EM13985510
1. Color blindness appears in 2% of the people in a certain population. How large must a random sample be in order to be 99% certain that a color-blind person is included in the sample?
2. A shirt manufacturer knows that, on the average, 2% of his product will not meet quality speci?cations. Find the greatest number of shirts constituting a lot that will have, with probability 0.95, fewer than ?ve defectives.
3. A random sample of size 100 is taken from a population with mean 1 and variance 0.04. Find the probability that the sample mean is between 0.99 and 1.
4. The lifetime X (in hours) of a certain electrical component has the pdf f(x) = (1/3)e-(1/3)x,x > 0. If a random sample of 36 is taken from these components, ?nd P(X 2).
5. A drug manufacturer receives a shipment of 10,000 calibrated "eyedroppers" for administer- ing the Sabin poliovirus vaccine. If the calibration mark is missing on 500 droppers, which are scattered randomly throughout the shipment, what is the probability that, at most, two defective droppers will be detected in a random sample of 125?
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In?nite population having the mean
: A random sample of size 150 is taken from an in?nite population having the mean μ = 15 and standard deviation σ = 2.5. What is the probability that X will be between 10.5 and 18.5?
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Calcualting the sampling distribution of the sample mean
: 1. Let the population be given by {1, 2, 3}. Let p(x) = 1/3 for x = 1, 2, 3. Take samples of size 3 with replacement. (a) Calculate μ and σ2. (b) Obtain the sampling distribution of the sample mean.
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Value of the ?nite population correction factor
: What is the probability of each sample in part (a), if each sample of size 2 is equally likely? Find the value of the ?nite population correction factor.
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Sampling distribution of the sample mean
: Let the population be given by the numbers {-2, -1, 0, 1, 2}. Take all random samples of size 3. (a) Without replacement, obtain the following in each case.
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Find the greatest number of shirts
: A shirt manufacturer knows that, on the average, 2% of his product will not meet quality speci?cations. Find the greatest number of shirts constituting a lot that will have, with probability 0.95, fewer than ?ve defectives.
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Failure of certain component follows the distribution
: Suppose that a failure of certain component follows the distribution f(x) = px(1 - p)x for x = 0, 1, and zero, elsewhere. How many components must one test in order that the sample mean X will lie within 0.4 of the true state of nature with probabili..
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Probability that the number of cars arriving
: Find, using Chebyshev's inequality, a lower bound for the probability that the number of cars arriving at the intersection in 1 hour is between 70 and 130.
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Variable with probability density function
: Let X be a random variable with probability density function 630x4(1 - x)4, 0 1,f(x) = 0, otherwise.
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Test the hypothesis that choice of major
: Test the hypothesis that the choice of the major by undergraduate students in this university is independent of their gender. Use α = 0.01.
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