A city is interested in building a parking garage in a certain area. Three hundred randomly selected residents from this area were asked, "Do you support the city's decision to build a parking garage in your area?" Of the 300 residents interviewed, 203 said no, 7 said yes, and 90 had no opinion. A large-sample z-confidence interval,p z *, was constructed from these data to estimate the proportion of the residents who support building a parking garage in a certain area. Which of the following statements is correct for this confidence interval?

This confidence interval is valid because a sample size of more than 30 was used.

This confidence interval is not valid because the quantity npis too small.

This confidence interval is valid because each area resident was asked the same question.

The confidence interval is valid because no conditions are required for constructing a large-sample confidence interval for a proportion.

This confidence interval is not valid because "no opinion" was included as a response category for the question.

Suppose that public opinion in a large city is 62% in favor of increasing taxes to support the after-school programs and 38% against such an increase. If an interview of the random sample of 450 people from this city is conducted, what is the approximate probability that more than 180 of these people will be against increasing taxes?