SOLUTION: 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. a. Calculate

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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.
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will fall above 92?
c. What is the probability that the sample mean will fall more than 8 points above the population mean of 100?
d. What is the probability that the sample mean will differ from the population mean by 4 points or more (in either direction)?
e. What sample mean has such a high value that the probability is .01 of obtaining one as high or higher?
f. Within what limits would the central 95% of all possible sample means fall?
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
Population:μ = 100 and σ = 30
sample size 36
a) SE = 30/sqrt(36) = 5
b) P(z > (92-100)/5) = normalcdf( -1.6, 100)
c) P(z > (108-100)/5) = normalcdf( 1.6, 100)
d) P(z < -4/5) - P( z < 4/5) = normalcdf(-.8,.8)
e) 5invNorm(.99) + 100 = X (probability is .01 of obtaining one as high or higher than X)
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