An article reported that in a large study carried out in the state of new york, approximately 60% of the study subjects lived within 1 mile of a hazardous waste site. let p denote the proportion of all new york residents who live within 1 mile of such a site, and suppose that p = 0.6.(c) when n = 400, what is p(0.55 ? p? ? 0.65)?

95.86%.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

This probability is the pvalue of Z when subtracted by the pvalue of Z when . So

X = 0.65

has a pvalue of 0.9793

X = 0.55

has a pvalue of 0.0207

So this probability is 0.9793 - 0.0207 = 0.9586 = 95.86%.