1. With regards to a standard normal distribution complete the following:
(a) Find P(z < 0), the proportion of the standard normal distribution below the z-score of 0. 0.5
(b) Find P(z > 1), the proportion of the standard normal distribution above the z-score of 1. 0.841344746
(c) Find P(-1 < z < 2). (d) Find P( z < 0.75). (e) Find the z-score that separates the lower 90% of standardized scores from the top 10% . . . that is find the z-score corresponding to P90, the 90th percentile value.
2. If the results on a nationally administered introductory statistics exam is normally distributed with a mean of 90 points and a standard deviation of 10 points, determine the following:
(a) Describe the graph of this distribution (if you can do so, produce an electronic sketch of the graph to the right, otherwise adequately describe the distribution graph through its shape and horizontal scale values.)
(b) Find the z-score for a single exam that had 115 points. Then find the z-score for one with 78 points.
(c) If x represents a possible point-score on the exam, find P(x < 110). P(x<90)=P(Z<90-100)/10)
(d) Find P(80 < x < 110) and give an interpretation of this value.
(e) What is the minimum number of points one must score on this exam if they want to be in the top 35% of all the scores?