Normal Distribution Directions: Solve each word problem. Show the conversion of raw score to z-score. Illustrate the appropriate shading of the normal curve for each problem. On the major examination in Statistics and Probability, a teacher gives a remark of Excellent to students who score between 90 and 95. The score of the examination have approximately a normal distribution with a mean of 84 and a standard deviation of 8. About what proportion of students get a remark of excellent? Monthly food expenditures for families in Caloocan City average 4 500 with a standard deviation of 750. Assuming that the monthly food expenditures are normally distributed. What percentages of these expenditures are between 3 900 and 5 850? The average cholesterol content of a certain duck eggs is 210 milligrams, and the standard deviation is 16 milligrams. Assume the variable is normally distributed. If a single egg is selected at random, find the probability that the cholesterol content will be greater than 205 milligrams