C. A manufacturing company firm produces LED lamps with a mean lifetime of 900 hours and a standard deviation of 55 hours. Find the probability that a random sample of 100 lamps will last on the average of 1. more than 915 hours a. What is the equivalent z-score of 915 hours? b. Show the z-score and corresponding raw score in the normal curve? Shade the area. c. Find the probability. 2. between 895 and 905 hours. a. What is the equivalent z-score of 895 and 905 hours? b. Show the z-score and corresponding raw score in the normal curve? Shade the area. c. Find the probability. D. A popular burger chain sells a particular soda brand using a machine that discharges an average of 500 ml per cup. If the amount of drink is normally distributed with a standard deviation of 35 ml. 1. What percent of the cups will contain more than $50 ml? 2. What is the number of cups that will contain more than $50 ml for 1500 drinks? 3. What percent of the cups will contain 490 to 530 ml? 4. What is the number of cups that will contain 490 to 530 ml for 1500 drinks! E. A survey tests on Leadership skills and on self-concept were administered to student- leaders. Both tests used a 10-point Likert-scale with 10 indicating the high scores for cach test. Scores for the student-leaders on the tests follow: Studen Self-concept | Leadership t Code Skills A 9.5 9.2 B 92 C 6.3 73 4.1 3.4 5.4 6.0 7 R 7.8 H 6.8 7.0 5.6 6.5 7.1 83 a. Computer. b. Interpret the result in terms of strength and direction. C. Find the regression line that will predict the leadership skill if the self-concept score is known. d. Predict the leadership skill of a student leader whose self-concept is 1.5