Do Prob. 1 with the last two constraints interchanged.
a. Find the mean and standard deviation of x for a binomial probability distribution with n = 16 and p = 0.5 ,b. Use a computer to construct the probability distribution and histogram for the binomial probability experiment with n _ 16 and p _ 0.5. ,c. Use a computer to randomly generate 200 samples of size 25 from a binomial probability distribution with n _ 16 and p _ 0.5. Calculate the mean of each sample. ,d. Construct a histogram and find the mean and standard deviation of the 200 sample means. ,e. Compare the probability distribution of x found in part b and the frequency distribution of in part d. Does your information support the CLT? Explain.
a. Find a value for e such that 95% of the apples in Exercise 7. 50 are within e units of the mean, 2.63. That is, find e such that,b. Find a value for E such that 95% of the samples of 100 apples taken from the orchard in Exercise 7. 50 will have mean values within E units of the mean, 2.63.That is, find E such that.
a. Describe the distribution of x, height of male college students. ,b. Find the proportion of male college students whose height is greater than 70 inches. ,c. Describe the distribution of , the mean of samples of size 16. ,d. Find the mean and standard error of the distribution.
a. Click “1” for “# Samples.” Note the four data values and their mean. Change “slow” to “batch” and take at least 1000 samples using the “500” for “# Samples.” ,b. What is the mean for the 1001 sample means? How close is it to the population mean, m? ,d. Does the histogram of sample means have an approximately normal shape?
Duke Energy manufactures and distributes electricity to customers in the United States and Latin America. Duke recently purchased Cinergy Corporation, which has generating facilities and energy customers in Indiana, Kentucky, and Ohio. For these customers Cinergy has been spending $725 to $750 million each year for the fuel needed to operate its coal-fired and gas-fired power plants; 92% to 95% of the fuel used is coal. In this region, Duke Energy uses 10 coal-burning generating plants: 5 located inland and 5 located on the Ohio River. Some plants have more than one generating unit. Duke Energy uses 28–29 million tons of coal per year at a cost of approximately $2 million every day in this region.,Managerial Report,Prepare a report that summarizes your recommendations regarding Duke Energy’s coal allocation problem. Be sure to include information and analysis for the following issues:,1. Determine how much coal to purchase from each of the mining companies and how it should be allocated to the generating units. What is the cost to purchase, deliver, and process the coal?,2. Compute the average cost of coal in cents per million BTUs for each generating unit (a measure of the cost of fuel for the generating units).,3. Compute the average number of BTUs per pound of coal received at each generating unit (a measure of the energy efficiency of the coal received at each unit).,4. Suppose that Duke Energy can purchase an additional 80,000 tons of coal from American Coal Sales as an “all or nothing deal” for $30 per ton. Should Duke Energy purchase the additional 80,000 tons of coal?,5. Suppose that Duke Energy learns that the energy content of the coal from Cyprus Amax is actually 13,000 BTUs per pound. Should Duke Energy revise its procurement plan?,6. Duke Energy has learned from its trading group that Duke Energy can sell 50,000 megawatt-hours of electricity over the grid (to other electricity suppliers) at a price of $30 per megawatt-hour. Should Duke Energy sell the electricity? If so, which generating units should produce the additional electricity?
A software engineer at Neverware, a company that replaces computers in schools with terminals connected to a server, is testing a new server to see if mean download times are decreased with the new server. When he compares a random sample of 20 times to the previous standard he gets a t-statistic of – 15. ,a) Explain what the t- statistic means in this context. ,b) Look up the 0.001 lower critical value for a t-statistic with 19 df and state your conclusion about the test. ,c) Why did you probably not need to look up the critical value in b) to reach your conclusion?
Discuss what happens to the M&D Chemicals problem (see Section 7.5) if the cost per gallon for product A is increased to $3.00 per gallon. What would you recommend? Explain.
A shipment of steel bars will be accepted if the mean breaking strength of a random sample of 10 steel bars is greater than 250 pounds per square inch. In the past, the breaking strength of such bars has had a mean of 235 and a variance of 400. ,a. Assuming that the breaking strengths are normally distributed, what is the probability that one randomly selected steel bar will have a breaking strength in the range from 245 to 255 pounds per square inch? ,b. What is the probability that the shipment will be accepted?