Question

A New York Times/CBS News Poll conducted in April 2007 reported that 72% of American would favor an increased federal tax on gasoline if it would reduce dependence of foreign oil. Use the normal approximation to answer the following!

a. For a sample of 200 Americans, what is the probability that at least 132 would favour such a tax? Don't forget the continuity correction

b. What is the mean of the sampling distribution?

c. What is the standard deviation of the sample distribution?

Answer 1

a. For a sample of 200 Americans, what is the probability that at least 132 would favour such a tax? Don't forget the continuity correction

The population proportion of success is p = 0.72 , and the sample size is n= 200 . We need to computePr( X ≥ 132 ) ):

The population mean is computed as:

and the population standard deviation is computed as:

Therefore, we get that

  

so then, we conclude that Pr( X ≥ 132 ) ≈0.9755, which ends the calculation of the requested probability

.

b. What is the mean of the sampling distribution?

c. What is the standard deviation of the sample distribution?