1) The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 21 points on this test, rounded to five decimal places? _________

(b) What is the 85 percentile of the distribution of test scores, rounded to three decimal places? __________

2) The Environmental Protection agency requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individually trucks according to a Normal distribution with mean 1.45 grams per mile driven and standard deviation 0.40 grams per mile.

(a) What is the 70th percentile for NOX exhaust, rounded to four decimal places? ________

(b) Find the interquartile range for the distribution of NOX levels in the exhaust of trucks rounded to four decimal places. _______

3) A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2 days with an approximately normal distribution.

(a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. ________

(b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places. _______