On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.3 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.

According to the U.S. Census, the average adult woman is the United States is 65 inches tall and the standard deviation is 3 inches.  If Zsike is 67 inches tall, what is her z-score?

You may need to use the appropriate technology to answer this question. Data were collected on the top 1,000 financial advisers. Company A had 239 people on the list and another company, Company B, had 121 people on the list. A sample of 16 of the advisers from Company A and 10 of the advisers from Company B showed that the advisers managed many very large accounts with a large variance in the total amount of funds managed. The standard deviation of the amount managed by advisers from Company A was s₁ = $583 million. The standard deviation of the amount managed by advisers from Company B was s₂ = $484 million. Conduct a hypothesis test at a = 0.10 to determine if there is a significant difference in the population variances for the amounts managed by the two companies. What is your conclusion about the variability in the amount of funds managed by advisers from the two firms? State the null and alternative hypotheses. 2 2 H₂:0 2 Find the value of the test statistic. (Round your answer…

A luxury furniture manufacture will make custom furniture for their customers. Pricing is based on the number of hours of skilled labor it takes to make a piece. The time it takes to make a custom couch is normally distributed with an average of 280 hours and a standard deviation of 40 hours.     What percent of custom couches take 255 hours or less to make?        How long would it take to build a couch that is in the 95th percentile?