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. 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 0. 8 hours per day unsupervised.


c. What percent of the children spend over 4. 1 hours per day unsupervised. % (Round to 2 decimal places)


d. 70% of all children spend at least how many hours per day unsupervised? hours