On the planet of Mercury, 4-year-olds average 3.2 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.6 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. a. What is the distribution of X? X - N( b. Find the probability that the child spends less than 2.3 hours per day unsupervised. c. What percent of the children spend over 4.8 hours per day unsupervised. % (Round to 2 decimal places) d. 63% of all children spend at least how many hours per day unsupervised? hours.

Students in the psychology department at General State University consumes an average of 7 sodas per day with a standard deviation of 2.5.  the distribution is normal.  Explain how you would go about answering the following questions (include your answer to the question in your response): How many sodas would an individual at the 75thpercentile drink per day?

A particular fruit's weights are normally distributed, with a mean of 786 grams and a standard deviation of 17 grams. The heaviest 18% of fruits weigh more than how many grams? Give your answer to the nearest gram.

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?