Reference no: EM131008767
1. Aplumber has found that his service call times follow a normal distribution with a mean of 45 minutes and a standard deviation of 15 minutes. A random sample of five service calls was taken.
a. What is the probability that the sample mean service time is more than 60 minutes? Why?
b. There is a 20 percent probability that the sample mean service time is fewer than how many minutes?
2. Suppose that a company produces a breakfast cereal whose true mean package weight is 20 ounces with a standard deviation of 0.6 ounces. Assume the population distribution of weights is normal and that you purchase four packages, which can be regarded as a random sample of all packages produced.
a. What is the probability that, on average, the contents of these four packages will weigh fewer than 19.4 ounces? Explain. What is the probability that, on average, the contents of these four packages will weigh more than 21.2 ounces? Explain.
b. What is the probability that, on average, the contents of these four packages will weigh between 19.5 and 20.5 ounces? Now suppose, instead, that you selected three of the four boxes at random to determine how sample size influences probability. What is the probability that the average contents of these three packages will weigh between 19.5 and 20.5 ounces? Explain.
3. Use the data set insurance1.dta and your knowledge of STATAto answer the following questions. After completing your work in STATA, paste the relevant STATA commands and resulting output from STATA's output window into your Word document after each question. Add any additional notes or explanation as necessary. (Please remember to use single-spaced Courier New 8-point font for the STATA output.)
a. How many observations does the data set contain? What is the range of ages for people in the dataset? What is the range of household incomes? For how many observations in the dataset is the reported household income $0?
b. How many individuals have private insurance? (Note the label on the variable "ins" in the variables window.) What percentage of the sample are these individuals? How does this percentage compare to your sense of the share of individuals with private insurance in the U.S. overall? Document "your sense" with the link to a reputable source on the internet that provides factual information about the proportion of people in the United States that have private health insurance.
c. Calculate the median, mean, and standard deviation of household income in this sample. To get more detailed descriptive statistics, open the help-file of the summarize command. Read the explanation of the ‘detail' option to understand what this option does. If still unclear, access the STATA manual by clicking the hyperlink on the top of the help file ([R] summarize) and look for some examples. Use what you learned to calculate the 10th percentile, 95th percentile, and skewness of household income.
d. Based on what you observe from part c., explain what you know about household income in this sample in a few sentences?
e. Create a histogram of the age variable. Choose an appropriate bin width and starting value. Add an appropriate title for your graph. Paste the graph into this Word document after the command that generates it. Explain what you know about the distribution of age in this sample, based on your histogram.