1) From the central limit theorem we see that the sampling distribution of the mean approaches a normal distribution with a mean of
"E(\\bar{X})=\\mu_{\\bar{X}}=\\mu=50 \\ kg"and a variance of
The standard deviation of the sampling distribution
2)
"P(48<\\bar{X}<53)=P\\bigg({48-50 \\over 6\/\\sqrt{30}}<Z<{53-50 \\over 6\/\\sqrt{30}}\\bigg)=""=P\\bigg(Z<{\\sqrt{30} \\over 2}\\bigg)-\\bigg(1-P\\bigg(Z<{\\sqrt{30} \\over 3}\\bigg)\\bigg)\\approx""\\approx0.9969-0.0339=0.9630"The number of sample that fall betweeen 48 and 53 kilograms
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The weight,x grams, of soup put into a carton by machine B is normally distributed with mean u grams and standard definition s grams . if p(x152)=0.6103, the value of u and s respectively
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