The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $36,807 and the median income is $34,270. A demographer decides to use the lognormal random variable to model this nonsymmetric income distribution. Let Y represent household income, where for a normally distributed X, Y = eX. In addition, suppose the standard deviation of household income is $12,000. Use this information to answer the following questions. a. Compute the mean and the standard deviation of X. b. What proportion of the people in the Bahamas have household income above the mean? c. What proportion of the people in the Bahamas have household income below $16,000? d. Compute the 70th percentile of the income distribution in the Bahamas.

The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratios†. 11 35 19 13 15 21 40 18 60 72 9 20 29 53 16 26 21 14 21 27 10 12 47 14 33 14 18 17 20 19 13 25 23 27 5 16 8 49 44 20 27 8 19 12 31 67 51 26 19 18 32   (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to four decimal places.)   x =   s =     (b) Find a 90% confidence interval for the P/E population mean ? of all large U.S. companies. (Round your answers to one decimal place.)   lower limit       upper limit         (c) Find a 99% confidence interval for the P/E population mean ? of all large U.S.…

In the year 2033, katy perry is a leading traveling nurse. Katy is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Katy takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using a = 0.05, answer the following questions. d) Using the appropriate level of confidence, what is the confidence interval? e) What is the interpretation (not your conclusions) of the confidence interval (in the context of the problem) you obtained in part c? f) What is the p value?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 19 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with ? = 0.36 gram.

is computed from a sample and is used to estimate a population parameter.

A researcher is interested in whether there is a difference between male and female college students in the amount of time spent doing volunteer work for the last 6 months. The researcher gathers a random sample of college students. The amount of time volunteering is measured in hours, which is an interval level-ratio and is normally distributed. Which statistical test should be used to analyze this data? a. Multiple regression b. paired samples t-test c. independent groups t-test d. Factorial ANOVA

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma.

1. Describe the key features of the normal curve and explain why the normal curve in real-life distributions nevermatches the model perfectly.

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At a= 0.10, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 32 31 26 31 34 41 25 24 290 27 30 33 30 29 28 30 25 23 OD. Ho p 32 Ha p2 32 Ha p< 32 Ha us 32 (b) Use technology to find the P-value. P = (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer.