Unformatted text preview: X is not known. Using Chebyshev’s theorem what can be said about the probability that X will be between 16 and 24 customers tomorrow? Example 4 A manufacturer of tires wants to advertise a mileage interval that excludes no more than 10% of the mileage on tires he sells. Suppose that μ = 25000 and σ = 4000. What interval would you suggest? (Use the Chebyshev’s theorem). [Ans. 12351,37649]. What would be the answer if it is known that the mileage follows the normal distribution? [Ans. 18420,31580] Example 5 A machine used to ﬁll cereal boxes dispenses on average μ ounces per box. The manufacturer wants the actual ounces dispensed, X , to be within 1 ounce of μ at least 75% of the time. What is the largest value of σ that can be tolerated if the manufacturer’s objectives are to be met? (Use Chebyshev’s theorem). [Ans. 1 2 ]....
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 Winter '10
 Christou
 Normal Distribution, Standard Deviation, Nicolas Christou, Nicolas Christou Chebyshev, Los Angeles Department of Statistics

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