10/17/2016 1. Assignment Print View Award: 11.11 points A random variable X follows the uniform distribution with a lower limit of 520 and an upper limit of 720. a. Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for Standard deviation to 4 decimal places and final answer to 2 decimal places.) Mean Standard deviation b. What is the probability that X is less than 630? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Probability rev: 11_02_2015_QC_CS31836, 03_22_2016_QC_CS46434 References Worksheet Difficulty: 2 Medium Learning Objective: 0602 Calculate and interpret probabilities for a random variable that follows the continuous uniform distribution. 2. Award: 11.11 points Find the following probabilities based on the standard normal variable Z. Use Table 1. (Round your answers to 4 decimal places.) a. b. c. d. P(Z > 0.67) P(Z 1.58) P(0 Z 1.40) P(0.79 Z 2.49) http://ezto.mheducation.com/hm.tpx 1/6 10/17/2016 Assignment Print View Hints Hint #1 3. Award: 11.11 points Find the following z values for the standard normal variable Z. Use Table 1. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) a. b. c. d. P(Z z) = 0.9186 P(Z > z) = 0.7254 P(z Z z) = 0.72 P(0 Z z) = 0.4813 Hints Hint #1 References Worksheet Difficulty: 2 Medium Learning Objective: 0604 Use the standard normal table (z table). 4. Award: 11.11 points Let X be normally distributed with mean = 19 and standard deviation = 10. Use Table 1. a. Find P(X 1). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) P(X 1) http://ezto.mheducation.com/hm.tpx 2/6 10/17/2016 Assignment Print View b. Find P(X > 4). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) P(X > 4) c. Find P(8 X 17). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) P(8 X 17) d. Find P(9 X 23). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) P(9 X 23) rev: 11_02_2015_QC_CS31836 References Worksheet Difficulty: 2 Medium Learning Objective: 0605 Calculate and interpret probabilities for a random variable that follows the normal distribution. 5. Award: 11.11 points Let X be normally distributed with mean = 132 and standard deviation = 35. Use Table 1. a. Find P(X 100). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) P(X 100) b. Find P(95 X 110). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) P(95 X 110) c. Find x such that P(X x) = 0.350. (Round "z" value and final answer to 2 decimal places.) x d. Find x such that P(X > x) = 0.810. (Round "z" value and final answer to 2 decimal places.) x rev: 11_05_2015_QC_CS31836 http://ezto.mheducation.com/hm.tpx 3/6 10/17/2016 Assignment Print View Hints Hint #1 References Worksheet Difficulty: 3 Hard Learning Objective: 0605 Calculate and interpret probabilities for a random variable that follows the normal distribution. 6. Award: 11.11 points The average high school teacher annual salary is $43,000 (Payscale.com, August 20, 2010). Let teacher salary be normally distributed with a standard deviation of $18,000. Use Table 1. a. What percentage of high school teachers make between $40,000 and $50,000? (Round "z" value and final answer to 2 decimal places.) Percentage of high school teachers % b. What percentage of high school teachers make more than $80,000? (Round "z" value and final answer to 2 decimal places.) Percentage of high school teachers % rev: 03_22_2016_QC_CS46434 References Worksheet Difficulty: 3 Hard Learning Objective: 0605 Calculate and interpret probabilities for a random variable that follows the normal distribution. 7. Award: 11.11 points According to a company's website, the top 25% of the candidates who take the entrance test will be called for an interview. You have just been called for an interview. The reported mean and standard deviation of the test scores are 70 and 9, respectively. What is the possible range for your test score if you assume that the scores are normally distributed? (Round "z" value and final answer to 2 decimal places.) http://ezto.mheducation.com/hm.tpx 4/6 10/17/2016 Assignment Print View Range and above rev: 11_02_2015_QC_CS31836 References Worksheet Difficulty: 3 Hard Learning Objective: 0605 Calculate and interpret probabilities for a random variable that follows the normal distribution. 8. Award: 11.11 points A packaging system fills boxes to an average weight of 18 ounces with a standard deviation of 0.3 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd, and 3rd quartiles of the box weight. (Round "z" value and final answer to 2 decimal places.) 1st quartile 2nd quartile 3rd quartile rev: 11_02_2015_QC_CS31836 References Worksheet Difficulty: 3 Hard Learning Objective: 0605 Calculate and interpret probabilities for a random variable that follows the normal distribution. 9. Award: 11.12 points The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 26 minutes and 13 minutes, respectively. Use Table 1. a. Find the probability that a randomly picked assembly takes between 19 and 30 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.) Probability b. http://ezto.mheducation.com/hm.tpx 5/6 10/17/2016 Assignment Print View It is unusual for the assembly time to be above 48 minutes or below 12 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.) Proportion of assembly times rev: 11_02_2015_QC_CS31836 http://ezto.mheducation.com/hm.tpx 6/6