91Ó°ÊÓ

Briefly explain the meaning of a population distribution and a sampling distribution. Give an example of each.

Consider a large population with \(\mu=90\) and \(\sigma=18\). Assuming \(n / N \leq, 05\), find the mean and standard deviation of the sample mean, \(\bar{x}\), for a sample size of a. 10 b. 35

A population of \(N=5000\) has \(\sigma=25 .\) In cach of the following cases, which formula will you usc to calculate \(\sigma_{\bar{x}}\) and why? Using the appropriate formula, calculate \(\sigma_{\bar{k}}\) for each of these cases. a. \(n=300\) b. \(n=100\)

What condition or conditions must hold true for the sampling distribution of the sample mean to be normal when the sample size is less than 30 ?

In an article by Laroche et al. (The Journal of the American Board of Family Medicine \(2007 ; 20: 9-15\) ), the average daily fat intake of U.S. adults with children in the household is \(91.4\) grams, with a standard deviation of \(93.25\) grams. These results are based on a sample of 3714 adults. Suppose that these results hold true for the current population distribution of daily fat intake of such adults, and that this distribution is strongly skewed to the right. Let \(\bar{x}\) be the average daily fat intake of 20 randomly selected U.S. adults with children in the household. Find the mean and the standard deviation of the sampling distribution of \(\bar{x}\). Do the same for a random sample of size \(75 .\) How do the shapes of the sampling distributions differ for the two sample sizes?

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. \(\bar{x}=132.05\)

According to the article by Laroche et al. mentioned in Exercise 7.37, the average daily fat intake of U.S. adults with children in the household is \(91.4\) grams, with a standard deviation of \(93.25\) grams. Find the probability that the average daily fat intake of a random sample of 75 U.S. adults with children in the household is a. less than 80 grams b. more than 100 grams c. 95 to 102 grams

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

As mentioned in Exercise \(7.33\), among college students who hold part-time jobs during the school year, the distribution of the time spent working per weck is approximately normally distributed with a mean of \(20.20\) hours and a standard deviation of \(2.6\) hours. Find the probability that the average time spent working per week for 18 randomly selected college students who hold part-time jobs during the school year is a. not within 1 hour of the population mean b. \(20.0\) to \(20.5\) hours c. at least 22 hours d. no more than 21 hours

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?