Subject: MAT 112: Statistics and Probability Topic: Normal Distribution, Areas under the normal curve, determining probabilities using areas under normal curve, computing or locating percentile, finding the area of the normal distribution

Test Ill. Finding the area under the normal curve (53 points) A. Given z - score. (9 points) Direction: Find the area of the following z - score. Show your complete solution on the space provide for. Scoring: (i) Graph - 1pt, (ii) Case#t - 1pt, (iii) Solving - 1pt -2.46 S z S -1.04 z 2 2.58 z - 1.49 B. Given normal - score. (20 points) Scoring: (i) Graph - 1pt, (ii) Case#t - 1pt, (iii) Find z - 1pt. (iv) Solving - 2pts 1. Given that X is a normally distributed with a mean of 100 and a standard deviation of 20. Find the probability that normal random variable X will have a value: Greater than 145 Between 76 and 127