1. The weight of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounces. a. What is the probability that a shoe weighs more than 13 ounces? b. What must the standard deviation of weight be in order for the company to state that 99.9% of its shoes are less than 13 ounces? 2. A study of 800 homeowners in a certain area showed that the average value of the homes was $82,000, and the standard deviation was $5000. If 50 homes are for sale, find the probability that the mean of the values of these homes is greater than $83,500. 3. A random sample of 20 acres gave a mean yield of sugarcane equal to 41.2 tons per acre with a standard deviation of 3 tons. Assuming that the yield of sugarcane per acre is normally distributed, a. Construct a 90% confidence interval for the population mean. b. What is the margin of error for this estimate in part a? 4. A federal report indicated that 27% of children ages 2 to 5 years had a good dietan increase over previous years. How large a sample is needed to estimate the true proportion of children with good diets within 2% with 95% confidence?

5. A random sample of stipends of teaching assistants in economics is listed. Is there sufficient evidence at the 0.05 level of significance to conclude that the average stipend differs from $15,000? The stipends listed (in dollars) are for the academic year. Sow all steps of hypothesis testing. 14,000 18,000 12,000 14,356 13,185 13,419 14,000 11,981 17,604 12,283 16,338 15,000 6. According to the Fiji Diabetes Association, 23.1% of Fijians aged 60 years or older had diabetes in 2017. A recent random sample of 200 Fijians aged 60 years or older showed that 52 of them have diabetes. Using a 5% significance level, perform a test of hypothesis to determine if the current percentage of Fijians aged 60 years or older who have diabetes is higher than that in 2017. Use the P-value method. 7. A real estate agent compares the selling prices of homes in two municipalities in southwestern Pennsylvania to see if there is a difference. The results of the study are shown. Is there enough evidence to reject the claim that the average cost of a home in both locations is the same? Use a = 0.01.