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

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

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
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

This note was uploaded on 03/17/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online