document.write( "Question 913353: 4. Given: μ = 100 and σ = 30 for a normally distributed population of observations. Suppose you randomly selected from this population a sample of size 36.
\n" ); document.write( "a. Calculate the standard error of the mean.
\n" ); document.write( "b. What is the probability that the sample mean will fall above 92?
\n" ); document.write( "c. What is the probability that the sample mean will fall more than 8 points above the population mean of 100?
\n" ); document.write( "d. What is the probability that the sample mean will differ from the population mean by 4 points or more (in either direction)?
\n" ); document.write( "e. What sample mean has such a high value that the probability is .01 of obtaining one as high or higher?
\n" ); document.write( "f. Within what limits would the central 95% of all possible sample means fall?
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Algebra.Com's Answer #554517 by ewatrrr(24785) $\"\"$ $\"About$

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Population:μ = 100 and σ = 30
\n" ); document.write( "sample size 36
\n" ); document.write( "a) SE = 30/sqrt(36) = 5
\n" ); document.write( "b) P(z > (92-100)/5) = normalcdf( -1.6, 100)
\n" ); document.write( "c) P(z > (108-100)/5) = normalcdf( 1.6, 100)
\n" ); document.write( "d) P(z < -4/5) - P( z < 4/5) = normalcdf(-.8,.8)
\n" ); document.write( "e) 5invNorm(.99) + 100 = X (probability is .01 of obtaining one as high or higher than X)
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