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A statistician wants to estimate the mean height h (in meters) of a population, based on n independent samples X1, . . . , Xn, chosen uniformly from the entire population. He uses the sample mean Mn = (X1 +···+Xn)/n as the estimate of h, and a rough guess of 1.0 meters for the standard deviation of the samples Xi.
a) How large should n be so that the standard deviation of Mn is at most 1 centimeter?
b) How large should n be so that Chebyshev's inequality guarantees that the estimate is within 5 centimeters from h, with probability at least 0.99?
The following problem develop the concept of determining the probability distribution of random variable and its mean and variance.
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At the 0.05 level of significance, is there evidence to suggest that the population mean waiting time to check out is less than 10.73 minutes?
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Avalon Bakery would like you to recommend how many loaves of its rye bread to bake at the beginning of each day. Each loaf costs the bakery $3.00 and can be sold for $6.00.
Promotion occurs on average every 10 days in a large corporation. What is the probability that the next promotion will occur within:
Formulate the hypotheses that can be used to determine whether union membership increased in 2006.
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