Question

"What do you think is the ideal number of children for a family to have?" A poll asked this question of 1070 randomly chosen adults. Slightly less than half (48%) thought that a total of two children was ideal. Suppose that

p = 0.48

is exactly true for the population of all adults. The polling company announced a margin of error of

±4 percentage

points for this poll. What is the probability that the sample proportion p̂ for an SRS of size

n = 1070

falls between 0.44 and 0.52? You see that it is likely, but not certain, that polls like this give results that are correct within their margin of error. (Round your answer to four decimal places.)

Answer 1

Solution:

We are given:

We are required to find .

Using the z-score formula, we have:

  

  

Now using the standard normal table, we have:

Therefore, the probability that the sample proportion p̂ for an SRS of size n = 1070 falls between 0.44 and 0.52 is 0.9912.