91Ó°ÊÓ

A population has mean 128 and standard deviation 22 . a. Find the mean and standard deviation of \(x-\) for samples of size 36 . b. Find the probability that the mean of a sample of size 36 will be within 10 units of the population mean, that is, between 118 and 138 .

Random samples of size 64 are drawn from a population with mean 32 and standard deviation \(5 .\) Find the mean and standard deviation of the sample mean.

Random samples of size 225 are drawn from a population in which the proportion with the characteristic of interest is \(0.25 .\) Decide whether or not the sample size is large enough to assume that the sample proportion \(\hat{\boldsymbol{p}}\) is normally distributed.

A random sample of size 121 is taken from a population in which the proportion with the characteristic of interest is \(p=0.47\). Find the indicated probabilities. a. \(P(0.45 \leq \widehat{P} \leq 0.50)\) b. \(P(\hat{P} \geq 0.50)\)

A normally distributed population has mean 57,800 and standard deviation \(750 .\) a. Find the probability that a single randomly selected element \(X\) of the population is between 57,000 and 58,000 . b. Find the mean and standard deviation of \(x-\) for samples of size 100 . c. Find the probability that the mean of a sample of size 100 drawn from this population is between 57,000 and \(58,000 .\)

A population has mean 72 and standard deviation 6 . a. Find the mean and standard deviation of \(x-\) for samples of size \(45 .\) b. Find the probability that the mean of a sample of size 45 will differ from the population mean 72 by at least 2 units, that is, is either less than 70 or more than 74 .