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COMPETENCIES: . Identifies regions under the normal curve corresponding to different standard normal values. (M11/12SP-IIIc-3) Converts a normal random variable to a standard normal variable and vice versa. (M11/12SP-IIIc-4) Computes probabilities and percentiles using the standard normal table. (M11/12SP-IIIc-d-1) DIRECTIONS: Read each problem carefully. Show your complete solution and present an illustration for each problem. 1. A group of 500 volunteers recorded an average age of 21.5 years and standard deviation of 9.6 years. Assumed the distribution is normally distributed. a. Find the number of volunteers with ages less than 20 years. b. Find the number of volunteers with ages greater than 22 years. C. Find the actual age of Roland if 85.31% of the volunteers are younger than him. d. If 2.5% of the volunteers are older than Shirley how old is she? e. Between what ages is the middle 40% of the volunteers? 2. The mean weight of 1000 students at a certain high school is 140 pounds and the variance is 100 pounds. Assuming that the weights are normally distributed, how many students weigh: a. Between 120 and 145 pounds? b. More than 150 pounds