Statistics help

The Acme Pro Office service provides temporary office personnel for many corporations. They have found that 88% of their invoices are paid within 10 working days by these corporations. Suppose the service randomly selects 8 of their invoices that are at least 10 working days old. Use this situation to answer the parts below. (a) Recognizing that this is a binomial situation, give the meaning 8 and F in this context. That is, define what you will classify as a "success" and what you will classify as a "failure" as it refers to paying invoices within 10 working days. 8 F (b) Next, give the values of n, p, and q. (Recall that q is the probability of failure in a trial.) n = p = q = (c) Construct the complete binomial probability distribution for this situation in a table out to the right. (d) Using your table, find the probability that exactly three of the chosen corporations paid within 10 working days. (e) Find the probability that at least six paid within 10 working days. (f) Find the probability that at most 4 paid within 10 working days. (9) Find the mean and standard deviation of this binomial probability distribution. (h) By writing a sentence, interpret the meaning of the mean value found in (g) as tied to the context of the Acme temp service and paid invoices. (i) Is it unusual to have only 6 of 8 invoices to have been paid within 10 days? Briefly explain your answer giving supporting numerical evidence. Px ro ems reae 0 ex s aper E If the results on a nationally administered introductory statistics exam are normally distributed with a mean of 65 points and a standard deviation of 4.5 points, determine the following: (a) Describe the graph of this distribution by telling the shape, naming the value at the peak, and giving the horizontal scale values three standard deviations to the left and three standard deviations to the right of the mean. (If you can do so, produce an electronic sketch of the graph to the right.) (b) Find the z-score for a single exam with a score of 58 points. Then nd the zscore for one with 70 points. (c) If x represents a possible pointscore on the exam, nd P(x > 70). (d) Find P (58 560). Based upon your result, state whether or not it is unusual for the length of a pregnancy to be greater than 560 days. (c) Suppose all possible samples of size 25, taken from the recorded lenths of pregnancies, are drawn and the mean is found for each resulting sample. Describe the shape and scaling on the graph of the resulting sampling distribution for the sample mean values. Hint: Apply the Central Limit Theorem! (d) Find the probability that the mean number of days of a randomly selected sample of 25 elephant pregnancy lengths is greater than 560 days. Based upon your result, state whether or not it is unusual to randomly select a sample of 25 elephant pregnancy lengths whose mean is greater than 570 days, and explain why you chose "unusual" or "not unusual" as your answer. (e) Find the probability that the mean from a sample of 25 elephant pregnancies will have a mean length between 515 and 535 days.7 12. Identify the type of sampling (stratified, systematic, convenience, or cluster) that best describes each of the following cases: a. Splitting all district fourth grade students into 4 separate classrooms, then randomly selecting ten students from each classroom to form a sample of 40 students. b. Standing near the entry of a local business and questioning every 10th person who walks by the business about brand recognition for the business. c. Asking all visitors to your web site to answer a short survey. d. An medical care researcher randomly selects 50 hospitals from the more than 6,000 across the U.S. then interviews all nurses at each of the selected hospitals. ted to text's Chapter 10 53. Suppose that a 95% confidence interval for a population mean u is given to be from 90 to 110. The 95% value in this statement indicates that: (choose the one best answer) A. When the statistical techniques in this unit are applied to build a 95% confidence interval around the mean of any randomly collected sample, we can only expect 95% of such calculated intervals to contain the true value of p . B. P (90