Question

murder IS IJ yculJ. person convicted of second-degree If the sentences are normally distributed with a standard deviation of 2.1 years, find these probabilities: a. A prison sentence is greater than 18 years. b. A prison sentence is less than 13 years. Source: The Book of Risks. 8. Doctoral Student Salaries Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard devia- tion of $1500, find these probabilities. a. The student makes more than $15,000 b. The student makes between $13,000 and $14,000 Source: U.S. Education Dept., Chronicle of Higher Education. 9. Miles Driven Annually The mean number of miles driven per vehicle annually in the United States is 12 404

Answer 1

Question 8. (a) P(X > 15000) Normal Distribution, μ-12837, σ-1500, we convert this to standard normal using z 15000-00283-= 1.442 1.44 P(Z > 1.44) Area to the right of 1.44 0.0749 1.44 P(X15000) P(Z > 1.44)-1- P(Z<144) 10.9251 0.0749 P(Z <1.44): in a z-table having area to the eft of z, locate 1.4 in the left most column. Move across the row to the right under column 0.04 and get value 0.9251 P(X > 15000)= 0.0749 = 7.49%

b) P(1300014000) Normal Distribution, μ-12837, σ-1500, we convert this to standard normal using z 13000 (12837) 0.108667 0.11 1500 14000(1283) 0.77333 0.78 1500 P(0.11 < Z < 0.78)= Area in between 0.11 and 0.78 0.7823- 0.54380.2385 0.782 0.5438 0.78 0.11 P(13000 < X < 14000) P(0.11 < Z < 0.78) = P(Z < 0.78)-P(Z < 0.11) 0.7823-0.5438-0.2385 P(Z < 0.78): in a z-table having area to the left of z, locate 0.7 in the left most column. Move across the row to the right under column 0.08 and get value 0.7823 P(Z< 0.11): in a z-table having area to the left of z, locate 0.1 in the left most column. Move across the row to the right under column 0.01 and get value 0.5438 P(13000 < X < 14000) 0.2385 = 23.85%