# Sampling Distribution

35. 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. Show the sampling distribution of _ , the proportion of late flights in a sample of1000flights

P

B. What is the probability that the sample proportion will be within .03 of the population proportion if a sample of size 1000 is selected?

C. Answer part (b) for a sample of 500 flights.

41. The mean television viewing time for Americans is 15 hours per week (Money, November 2003.) Suppose a sample of 60 Americans is taken to further investigates viewing habits.

Assume the population standard deviation for weekly viewing time is = 4 hours.

A. What is the probability the sample mean will be within 1 hour of the population mean?

B. What is the probability the sample mean will be within 45 minutes of the population mean?

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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. Show the sampling distribution of P, the proportion of late flights in a sample of1000flights

population proportion=p= 25.00%

q=1-p= 75.00%

n=sample size= 1000

σp=standard error of proportion=√(pq/n)= 1.369% =√ ( 25.% * 75.% / 1000)

z=(proportion -population proportion)/σp= 1

Probability value corresponding to Z = 1 is 68.27% 0r 0.6827

proportion=mean proportion+zσp= 26.369% =0.25+(1*0.01369)

proportion=mean proportion-zσp= 23.631% =0.25-(1*0.01369)

Thus there is a 68.27% probability that the proportuion of flights are late is between 23.631% and 26.369%

z=(proportion -population proportion)/σp= 2

Probability value corresponding to Z = 2 is 95.45% 0r 0.9545

proportion=mean proportion+zσp= 27.738% =0.25+(2*0.01369)

proportion=mean proportion-zσp= 22.262% =0.25-(2*0.01369)

Thus there is a 95.45% probability that the proportuion of flights are late is between 22.262% and ...

#### Solution Summary

The solution calculates the probability of finding a sample mean within a particular range from the population mean, probability of finding a sample proportion within a particular range from population proportion.