91Ó°ÊÓ

A population has a normal distribution. A sample of size \(n\) is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases. a. \(n=94\) b. \(n=11\)

The amounts of electricity bills for all households in a particular city have an approximate normal distribution with a mean of \(\$ 140\) and a standard deviation of \(\$ 30\). Let \(\bar{x}\) be the mean amount of electricity bills for a random sample of 25 households selected from this city. Find the mean and standard deviation of \(\bar{x}\), and comment on the shape of its sampling distribution.

For a population, \(N=10,000, \mu=124\), and \(\sigma=18\). Find the \(z\) value for each of the following for \(n=36\). a. \(\bar{x}=128.60\) b. \(\bar{x}=119.30\) c. \(\bar{x}=116.88\) d. \(\bar{x}=132.05\)

Let \(x\) be a continuous random variable that has a normal distribution with \(\mu=75\) and \(\sigma=14\). Assuming \(n / N \leq .05\), find the probability that the sample mean, \(\bar{x}\), for a random sample of 20 taken from this population will be a. between \(68.5\) and \(77.3\) b. less than \(72.4\)

The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of \(3.02\) and a standard deviation of \(.29\). Find the probability that the mean GPA of a random sample of 20 students selected from this university is a. \(3.10\) or higher b. \(2.90\) or lower c. \(2.95\) to \(3.11\)

The times that college students spend studying per week have a distribution that is skewed to the right with a mean of \(8.4\) hours and a standard deviation of \(2.7\) hours. Find the probability that the mean time spent studying per week for a random sample of 45 students would be a. between 8 and 9 hours b. less than 8 hours

The amounts of electricity bills for all households in a city have a skewed probability distribution with a mean of \(\$ 140\) and a standard deviation of \(\$ 30\). Find the probability that the mean amount of electric bills for a random sample of 75 households selected from this city will be a. between \(\$ 132\) and \(\$ 136\) b. within \(\$ 6\) of the population mean c. more than the population mean by at least \(\$ 4\)

Johnson Electronics Corporation makes electric tubes. It is known that the standard deviation of the lives of these tubes is 150 hours. The company's research department takes a sample of 100 such tubes and finds that the mean life of these tubes is 2250 hours. What is the probability that this sample mean is within 25 hours of the mean life of all tubes produced by this company?

A machine at Katz Steel Corporation makes 3 -inch-long nails. The probability distribution of the lengths of these nails is approximately normal with a mean of 3 inches and a standard deviation of \(.1\) inch. The quality control inspector takes a sample of 25 nails once a week and calculates the mean length of these nails. If the mean of this sample is either less than \(2.95\) inches or greater than \(3.05\) inches, the inspector concludes that the machine needs an adjustment. What is the probability that based on a sample of 25 nails, the inspector will conclude that the machine needs an adjustment?

In a population of 18,700 subjects, \(30 \%\) possess a certain characteristic. In a sample of 250 subjects selected from this population, \(25 \%\) possess the same characteristic. How many subjects in the population and sample, respectively, possess this characteristic?