Statistics/Probability H/W Solution Correct Answers

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Statistics/Probability H/WSolution Correct AnswersInstructions: Please show all work, this includes formulas used and writing down whatyou entered into the calculator in case you use the calculator to solve problems.1.The mean output of an amplifier is 181 watts.It has σ = 10 watts.If 98 amplifiersare sampled, what is the probability that the average output is between 178.9 and183.1 watts?(6 points)2.Suppose that 56% of students at a university are in the College of Business.Asample of 803 students is taken.What is the probability that the sample proportionof students in the College of Business is greater than 53%? (6 points)3.Given a confidence interval for a population mean of 11.78 < μ < 21.96, determinethe original point estimate for the interval and the margin of error.(6 points)4.A chemist would like a margin of error for his experiment on chemical viscosity tobe no more than 0.6217.How large a sample must he use ifσ= 0.858 and hewould like to have a 95% confidence level?(6 points)5.When must a critical t value be used rather than a critical z value? (4 points)6.The average GPA for a sample of 100 high school students considering attending alocal university is 3.21 with s = 0.17.Determine a 99% confidence interval for thepopulation mean.Interpret the interval. (8 points)7.The following is a random sample of the annual salaries of high school counselors inthe US.Assuming that the distribution of salaries is approximately normal, constructa 90% confidence interval for the mean salary of high school counselors across theUS.Interpret the interval.(8 points)$51,050

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$38,740$65,360$42,640$55,340$32,980$49,5408.Case studies show that out of 10,351 convicts who escaped from US prisons, only7867 were recaptured.Let p represent the proportions of all escaped convicts whowill eventually be recaptured.Find a point estimate for p.Find a 99% confidenceinterval for p.Interpret the interval.(8 points)9.Samples of diameters taken from 11 gaskets off an assembly line are:9.7, 10.6, 10.3 10.4, 9.9, 9.7, 10.1, 10.1, 10.4, 9.4 and 9.7Build a 95% confidence interval for the population standard deviation.Please refer to thechi-square table.(8 points)10.Frozen Food Company uses a machine that packages blueberries in 7 poundportions.A sample of 30 packages has a variance of 0.1225 pounds.Construct a90% confidence interval for the population variance.Please refer to the chi–squaretable.(8 points)Formulae