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# chp16 - Normal Distribution Example 2 Statistical Quality...

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Statistical Quality Control II FScN Food Quality November 17, 2000 Normal Distribution: Example 2 A preserve process consistently produces jars of jelly-beans with a mean headspace of 5.83/32 inch and a standard deviation of 1.64/32 inch. a) In a random sample of 100 jars, what is the probability that the average headspace will be less than 5/32 inch? b) How large a sample must be taken to be 95% sure that the sample mean does not fall below 5.3/32 inch Z= (X - µ ) σ / n Normal Distribution: Example 2 Normal Approximation to Binomial Distribution • If µ = np > 5, then Poisson is not satisfactory as Binomial distribution Normal distribution can be used if: p and q are close n is large • Formulas: µ = np and σ = npq Normal Approximation to Binomial Distribution: Example If 8% of a packaged product is known to be underweight, what is the probability that a random sample of 100 packages will contain: a) 14 or more underweight packages b) 4 or fewer underweight packages.

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