View the step-by-step solution to:

ST 558 Probability and Statistics Exam # 2 Possible points: 100 [SHOW ALL OF YOUR WORK FOR PARTIAL CREDIT] 1. The width of a slot of a duralumin

any other than 1, 5 or 6. I got those. please help
ST 558 Probability and Statistics Exam # 2 Possible points: 100 [SHOW ALL OF YOUR WORK FOR PARTIAL CREDIT] 1. The width of a slot of a duralumin forging is ( in inches) normally distributed with μ = 0 . 9000 and σ = 0 . 0030 . The specification limits were given as 0 . 9000 ± 0 . 0050 . (a) What percentage of forgings will be defective? (b) What is the maximum allowable value of σ that will permit no more than 1 in 100 defectives when the widths are normally distributed with μ = 0 . 9000 and σ ? 2. One thousand independent rolls of a fair die will be made. Compute an approximation to the probability that number 6 will appear between 150 and 200 times. If number 6 appears exactly 200 times, find the probability that number 5 will appear less than 150 times. 3. (a) Suppose that X is a normal random variable with mean 5. If P ( X > 9) = 0 . 2 , find the variance of X. (b) The average life of a bread-making machine is 7 years, with a stan- dard deviation of 1 year. Assuming that the lives of these machines follow approximately a normal distribution , find (i) the probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2 years (ii) For what value to the right of which 15% of the means computed from random samples of size 9 would fall. 4. In an experiment with a new tranquilizer, the pulse rates (per minute) of 12 patients were determined before they were given the tranquilizer and again 5 minutes later, and their pulse rates were found to be re- duced on the average by 7.2 beats with a standard deviation of 1.8. At the level of significance 0.05, do we have significance evidence that the mean pulse reduction with this tranquilizer is less than 9.0 beats? Also, find 95% confidence interval for the average pulse rate. 1
Background image of page 1
5. A medical research team conducted a study to test the effect of a choles- terol reducing medication. At the end of the study, the researchers found that of the 4700 subjects who took the medication, 301 died of heart disease. Of the 4300 subjects who took a placebo, 357 died of heart disease. At α = 0 . 01 , can you conclude that the death rate is lower for those who took the medication than for those who the placebo? Construct a 95% confidence interval for the two population proportions. 6. A manufacturer claims that the calling range (in miles) of its 900-MHz cordless telephone is greater than that of its leading competitor. You perform a study using 14 phones from the manufacturer had a mean 1275 with a standard deviation of 45. The mean for 16 similar phones from its competitor was 1250 with a standard deviation 30. At α = 0 . 05 , is there enough evidence to support the manufacturer’s claim? Assume the population variances are equal. Find a 95% confidence interval for the difference of two population means. 7. The random variable X has probability density function f ( X ) = ± aX + bX 2 for 0 < X < 1 0 elsewhere If E(X) =0.6, then (a) Find constants a and b (b) Find P ( X 0 . 5) . (c) Find V ar ( X ) . 8. The joint density of X and Y is given by f ( X, Y ) = ± C ( Y - X ) e - Y for - Y < X < Y, 0 < Y < 0 elsewhere (a) Find C. (b) Find marginal density functions for X and Y. (c) Find E(X) and E(Y). Hint: Γ( α ) = R 0 e - u u α - 1 du and Γ( α ) = ( α - 1)! 2
Background image of page 2
Show entire document

Top Answer

Hello, We can only answer your free 3 questions per day one at a time. Please re-submit an individual question here:... View the full answer

Sign up to view the full answer

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.


Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask a homework question - tutors are online