A production process is checked periodically by a quality control inspector. the

Question

A production process is checked periodically by a quality control inspector. the inspector selects simple random samples of 30 finished products and computes the sample mean product weight. If test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process? What is the population mean? (to 1 decimal) What is the population standard deviation (to 2 decimals)?

Explanation / Answer

it is shown that 5% values are over 2.1 pounds and 5% are under 1.9 pounds

so stasttically that means

P( X > 2.1,  ; ) = 0.05 and P( X 1.9; ; ) = 0.05

where   is mean of the sample and is the standerd deviation of the sample.

so mean can be calculated easily = (2.1 + 1.9)/2 = 2.0

and as we can interpret P(1.9 <x < 2.1; 2.0; ) = 0.90 by normal distribution the Z value for 90% confidence interval is 1.65

so = (2.1 -2) /1.65 = 0.06

standerd deviation of the sample mean= 0.06

and by that standerd deviation of population mean = 0.06 * (30) 0.5 = 0.33

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