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stattistics problem (algorithmic)?
The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p = .25.
Calculate σ( p¯) with a sample size of 1,000 flights (to 4 decimals).
What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 1,000 is selected (to 4 decimals)?
What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 500 is selected (to 4 decimals)?
1 Answer
- Anonymous10 years agoFavorite Answer
I'm going to attempt this but I'm not certain about it. The standard deviation would be sqrt of (pq/n) or
sqrt (.25 X .75/1000) that is sqrt of .0001875 which is .0137 rounded to 4 places. For the next one find the z score of .03 from the mean; take .03 and divide by the standard deviation and you get 2.1909. So you are looking at the probability of being between -2.19 and 2.19 standard deviations of the mean. Take the probability of being less than 2.19 standard deviations above the mean which is
.9857 and subtract the porobability of being more than 2.19 sd's below the mean , which is .0143, and get .9714. for the last part you are going to have to figure the sd using 500 for n and then do the same thing.