Homework #10 Name: Normal Distribution 1. P(-0.23 g 2 g 1.53) : 2. P( z> -1.18) = 3. Find the value of 20, such that P( -20 g 2 3 Zn) : 0.86 4. Find the value of 20, such that P(z g 20) = 0.2877r 5. The random variable X is normally distributed with mean 95 and standard deviation 9. a) What is the probability that a value of X chosen at random will be between 85 and 100? b) What is the probability that a value of X chosen at random will be less than 86? 6. The scores on a placement test have a mound-shaped distribution with mean 350 and standard deviation 40. a) What percentage of people taking this exam will have scores of 330 or greater? b) What percentage of the people taking this test will have scores between 325 and 390? 7. A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximately normally distributed with a mean of 30 and a standard deviation of 8. The higher the score the greater the motivation to do well in school. a) What percentage of students taking this test will have scores below 20'? b) John is told that 44% of the students taking the test have higher motivation scores than he does? What was John's score? 8. A population of 29 year-old males has a mean salary of $39,500 with a standard deviation of $3,200. If a sample of 100 men is taken: a) What is the probability their mean salaries will be less than $39,000? b) What is the probability their mean salaries will be greater than $39,000? c) 'What is the probability their mean salaries will be between $39000 and $39,500? 9. There are 250 dogs at a dog show who weigh an average of 15 pounds. with a standard deviation of 6 pounds. If 10 dogs are chosen at random, what is the probability they have an average weight of greater than 10 pounds and less than 15 pounds