The Democrat and Chronicle reported that 25% of the flights arriving at the San
ID: 3350303 • Letter: T
Question
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.A) What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 400 is selected (to 4 decimals)? 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.
A) What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 400 is selected (to 4 decimals)? 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.
A) What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 400 is selected (to 4 decimals)?
Explanation / Answer
Result:
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.
A) What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 400 is selected (to 4 decimals)?
Standard error = sqrt(p*(1-p)/n) = sqrt(0.25*0.75/400) = 0.0217
z =0.03/0.0217 =1.38
The required probability P( -0.03 <P-p <0.03)
=P( -1.38 < z <1.38) = P( z < 1.38) – P( z < -1.38)
=0.9162 -0.0838
=0.8324
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