EC507—Statistics for Economists Sprimg 2010 Problem Set 4 1.X is a normally distributed random variable with mean equal to 7 and variance equal to 25. You draw a random sample of size 100. a.Calculate )86(≤≤XPand)86(≤≤XP. b.Explain intuitively why the two probabilities differ.
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2.Each minute a machine produces a length of rope with mean of 4 feet and standard deviation of 5 inches. Assuming that the amounts produced in different minutes are independent and identically distributed, approximate the probability that the machine will produce at least 250 feet in one hour.