INTRO STAT THEORY I
INTRO STAT THEORY I STAT 702
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This 1 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 702 at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/229677/stat-702-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.
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Date Created: 10/26/15
Examples 3 and 4 from September 21st 3 Five of 20 presses are being tested for excessive wear a If four of the 20 are actually defective what is the probability that none of the defectives will be found So this is a hypergeometric distribution with N20 n5 r4 and the question is seeking PX0 416 16 1 0 5 gtxlt gtxlt gtxlt wz zwwzm r20 20 20191817 K5 515 b Give a reasonable 95 range for how many defectives you would expect to find in the ve sampled A rough estimate would be the mean 2 standard deviations In this case the mean is np5420l and the variance can be written nplpNnNl5281519631579 making the sd7947l94 The rough interval would thus be 1 1593 Since only integers can happen this becomes 0 to 2 4 Approximately 31 of the South Carolina population is of Hispanic or Latino origin a How many South Carolinians would you need to sample on average before you arrive at your rst Hispanic If we act like this is a binomial experiment assuming any sample we take is much smaller than the entire population then this is a geometric distribution and the problem is asking for the mean ulpl03l32258 b Give a reasonable 95 range of how many you would need to sample to have 10 Hispanics included Again assuming a binomial is a good approximation this is now a negative binomial problem As in 3b we need to nd the mean and variances The mean is rlp10l03l Z32258 and the variance is rl pp21010310312 1008325 making the sd1004154 A rough interval would thus be 32258 20083 which rounds to 122 to 523