(Solved): Out of 300 people sampled, 45 had children. Based on this, construct a \( 90 \% \) confidence inter ...

Out of 300 people sampled, 45 had children. Based on this, construct a \( 90 \% \) confidence interval for the true population proportion of people with children. Preliminary: a. Is it safe to assume that \( n \leq 5 \% \) of all people with children? No Yes b. Verify \( n \hat{p}(1-\hat{p}) \geq 10 \). Round your answer to one decimat place. \( n \hat{p}(1-\hat{p})= \) Confidence Interval: What is the \( 90 x \) confidence interval to estimate the population proportion? Round your answer to three decimal places. A Food Marketing Institute found that \( 35 \% \) of households spend more than \( \$ 125 \) a week on groceries. Assume the population proportion is \( 0.35 \) and a simple random sample of 399 households is selected from the population. What is the probability that the sample proportion of households spending more than \( \$ 125 \mathrm{a} \). week is less than \( 0.34 \) ? There is a probability that the sample proportion of households spending more than \( \$ 125 \) a week is less than \( 0.34 \). Round the answer to 4 decimal places. In an effort to cut costs and improve profits, any US companies have been turning to outsourcing. In fact, according to Purchasing magazine, \( 54 \% \) of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 555 of these companies are contacted. a. What is the probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years? Round answer to four decimal places. b. What is the probability that 285 or more companies outsourced some part of their manufacturine process in the past two or three years? Round answer to four decimal place. c. What is the probability that \( 48 \% \) or less of these companies outsourced some part of their manufacturine orocess in the past two or three years? Round answer to four decimal places.