A researcher believes that a greater proportion of construction companies in the northeast are using certified lumber in home construction projects compared to companies in the southeast. She collected a random sample of 175 companies in the southeast and found that 76 used at least 30% certified lumber. She collected another random sample of 116 companies from the northeast and found that 67 used at least 30% certified lumber. Find P-value if we want to test the researcher’s claim that an equal proportion of companies in the northeast use at least 30% certified lumber compared to the southeast using α = 0.05. Round to three decimal places.

Let P (Z < 2.41) = 0.992), P (Z < −1.57) = 0.058.

Suppose that X has a Poisson distribution with a

mean of 64. 

Use a normal distribution to approximate the probability P(X > 72).