# Normal Distribution

#1

With regards to a standard normal distribution complete the following:

(a) Find P(z < 0), the percentage of the standard normal distribution below the z-score of 0.

(b) Find P(z < 1.65), the percentage of the standard normal distribution below the z-score of 1.65

(c) Find P(-3 < z < 3).

(d) Find P( z > 2).

(e) Find the z-score that separates the lower 75% of standarized scores from the top 25% . . . that is find the z-score corresponding to P75, the 75th percentile value in the standard normal distribution.

#2

If the results on a nationally administered university entry exam are normally distributed with a mean of 45 points and a standard deviation of 4 points, determine the following:

(a) Describe the graph of this distribution. If you can do so easily, feel free to give a sketch of the graph as demonstrated in the Excel guides and the answer keys to the text problems, otherwise just describe the distribution graph through its shape and important horizontal scale values.)

(b) Find the z-score for a single exam that had 37 points. Then find the z-score for one with 55 points.

(c) If x represents a possible point-score from a randomly chosen exam, find P(x < 41).

(d) Find P(40 < x < 50) and give an interpretation of this value.

(e) Suppose a certain university requires one to score in the top 35% of all such scores to be admitted. What is the minimum number of points one must score on this exam for admission?

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#### Solution Summary

Corresponding z-scores percentiles are determined.