# hw2_1 - and 0.9030 cm A sample of 10 shafts was taken from...

This preview shows pages 1–2. Sign up to view the full content.

Homework 2 (due Feb. 5) 1. The probability theorist is shooting a basketball from behind the midcourt. He has established that the probability of his hitting such a shot is equal to 0.05. Assume that the results of different shots are independent on each other. a) What is the probability of his hitting 2 or more shots out of 20? Calculate this exactly and using normal approximation. Comment on the adequacy of the latter. b) What is the probability of his hitting 20 or more shots out of 200. Calculate this exactly and using normal approximation. Is the normal ap- proximation adequate this time? 2. A random variable X has a binomial distribution. a) Suppose n = 20 and p = 0 . 1. Calculate P (5 X 10) exactly. Next, calculate it using normal approximation (with the adjustment). Is normal a good approximation based on this result. b) Suppose now that n = 2000 and p = 0 . 1 Calculate P (220 X 250) exactly and using normal approximation. Comment on the precision of the normal approximation. Compare with a). 3. A shaft is considered to be in-spec if its diameter is between 0.8970

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: and 0.9030 cm. A sample of 10 shafts was taken from a shaft-producing machine. Their diameters turned out to be: 0.9030, 0.9032, 0.9031, 0.9039, 0.9030, 0.9038, 0.9002, 0.9020, 0.9018, 0.8996. a) Calculate an unbiased estimate of the proportion of in-spec shafts from this sample. b) Calculate unbiased estimates of the mean and variance of the shaft diameter produced by the machine. c) Assuming that the distribution of shaft diameters is normal, and that it is impossible to change the variance, calculate the percentage of in-spec shafts that the machine would produce if we adjusted the mean optimally. 4. Suppose a 1700 insurer wants to pin down the probability of a ship 1 being lost with a precision of 0.01 with probability of 99%. How many past cases does he need to look at in the worst case? What is the answer if he believes that the probability is no more than 0.03? 2...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern