Using the Normal Distribution · Exercise 27

In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly select one Chinese four-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.

(a) In words, define the random variable X.
(b) X ~ _____(_____,_____)
(c) Find the probability that the child spends less than one hour per day unsupervised. Sketch the graph, and write the probability statement.
(d) What percent of the children spend over ten hours per day unsupervised?
(e) Seventy percent of the children spend at least how long per day unsupervised?

OpenStax, Introductory Statistics 2e · §6.2 Using the Normal Distribution · Exercise 27