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(114 points) Suppose that X is normally distributed with mean 95 and standard deviation 16 A. What is the probability that X is greater than 123.64? B. What value of X does only the top 10% exceed? X = (115 points) Suppose the scores of students on a Statistics course are Normally distributed with a mean of 367 and a standard deviation of 60. What percentage of the students scored between 247 and 367 on the exam? (Give your answer to 3 significant figures.) percent. (114 points) Let X be a random number between 0 and 1 produced by the idealized uniform random number generator. Use the density curve for X . shown below, to find the probabilities: (Click on the image for a larger view.) (a) P(X > 0.8) = (b) P(X = 0.25) = An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.12 ppm and a standard deviation of 3.5 ppm. Suppose that you draw a random sample of 11 printers. Part i) Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 17.42 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion) C] Part ii) Use normal approximation to find the probability that more than 41.1% of the sampled printers operate at the advertised speed (i.e. the printing speed is equal to or greater than 18 ppm) 0 A. 0.5025 Q B. 0.4730 0 c. 0.4975 0 D. 0.5270 A statistics practitioner took a random sample of 53 observations from a population whose standard deviation is 22 and computed the sample mean to be 1 10. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. A. Estimate the population mean with 95% confidence. Confidence Interval = B. Estimate the population mean with 95% confidence, changing the population standard deviation to 41; Confidence Interval = C. Estimate the population mean with 95% confidence, changing the population standard deviation to 9; Confidence Interval = How many rounds of golf do those physicians who play golf play per year? A survey of 12 physicians revealed the following numbers: 6, 40, 17, 4, 35, 39, 21, 13, 18, 31, 11, 52 Estimate with 91% confidence the mean number of rounds played per year by physicians, assuming that the population is normally distributed with a standard deviation of 7. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. Confidence Interval = Use the given data to find the 95% confidence interval estimate of the population mean [L Assume that the population has a normal distribution. IQ scores of professional athletes: Sample size n = 30 Mean 3 = 105 Standard deviation 5 = 10