$.33 The chemical benzene is highly toxic to hu- However, it is used in the manu
ID: 3370474 • Letter: #
Question
$.33 The chemical benzene is highly toxic to hu- However, it is used in the manufacture of many edicine dyes, leather, and coverings. Government regulations dictate that for any production process in- volving benzene, the water in the output of the process must not exceed 7950 parts per million (ppm) of bern- ne. For a particular process of concern, the water sample was collected by a manufacturer 25 times ran- domly and the sample average " was 7960 ppm. It is known from historical data that the standard deviation ze ? is 100 ppm. (a) What is the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? Use the Central Limit Theorem. (b) Is an observed 7960 in this experiment firm idence that the population mean for the process
Explanation / Answer
Here , X? follows normal( 7960 , 1002/25 )
(a) we need to find P( X? > 7950 ) = P( ( X? - 7960 )/ ( 100/250.5) > ( 7950 - 7960 )/ ( 100/250.5) )
= P( Z > -10/20) = P(Z > -0.5 ) = 0.691462
(b) Since the probability value = 0.691462 > 0.05 ( level of significance) , we can say that X? = 7960 in this experiment firm evidence that the population mean for the process.
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