# chap04 - PROBLEM 4.1 KNOWN N > 1000 x= 9.2 units Sx = 1.1...

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4-1 PROBLEM 4.1 KNOWN: N > 1000; x = 9.2 units ; S x = 1.1 units FIND: Range of x in which 50% of all measurements should fall. ASSUMPTIONS: Measurand follows a normal density function Data set sufficiently large such that x x’ and S x σ SOLUTION By assuming that the data is sufficiently large such that its population behaves as an infinite population, we can find the interval defined by x' - z 1 σ x i x' + z 1 σ as follows. We can find P(x' + z 1 σ ) from the one-sided integral solution to This solution is given in Table 4.3 for p(z 1 ) = 0.25 (one half of the 50% probability sought) as z 1 = 0.674. Then, we d β e ] [2 1 ) P(z 1 2 Z 0 /2 β 1/2 1 π =

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4-2 should expect that 50% of the x i values lie in the interval given by 9.2 – 0.7425 x i 9.2 + 0.7425 (50%) COMMENT We can see from Table 4.4 that as N becomes large the value for t approaches a value given by z 1 .