Question: Amber Cagle BMDS 3370 Chapter 6 - Continuous Random Variables 6.20 a-i If the random variable z has a standard normal distribution, sketch and find

Amber Cagle BMDS 3370 Chapter 6 - Continuous Random Variables 6.20 a-i If the random variable z has a standard normal distribution, sketch and find each of the following probabilities: a. b. c. d. e. f. g. h. i. P(0 < z < 1.5) P(z > 2) P(z < 1.5) P(z > - 1) P(z < - 3) P(-1 < z < 1) P(-2.5 < z < .5) P(1.5 < z < 2) P(-2 < z < -.5) 6.22 a-h Suppose that the random variable x is normally distributed with mean m = 1,000 and standard deviation o = 100. Sketch and find each of the following probabilities: a. b. c. d. e. f. g. h. P(1,000 < x < 1,200) P(x > 1,257) P(x < 1,035) P(857 < x < 1,183 P(x < 700) P(812 < x < 913) P(x > 891) P(1,050 < x < 1,250) Page 1 of 2 Amber Cagle BMDS 3370 6.24 a-c Stanford-Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 16. a. Sketch the distribution of Stanford-Binet IQ test scores. b. What score (percentage) would you have to have to be in the top 10%? c. Find the probability that a randomly selected person has an IQ test score (1) Over 140. (2) Under 88. (3) Between 72 and 128. (4) Within 1.5 standard deviations of the mean. 6.25 a-b Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 800 boxes and a standard deviation of 75 boxes. a. What is the probability that weekly demand is (1) 959 boxes or less? (2) More than 1,004 boxes? (3) Less than 650 boxes or greater than 950 boxes? b. What score (percentage) would you have to have to be in the top 20%? Page 2 of 2

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