1.3 MATH-138 Statistics Directions: On a separate sheet of paper, write out your solutions to the questions below. Late assignments will receive a grade of zero unless prior arrangements are made with me. This assignment is worth 38 points. Do not make these calculations by hand. Instead, use the proper command in your graphing calculator, unless otherwise noted. Write out what you entered in your calculator. If you complete the probabilities by hand, you will receive no credit for that part of the problem. 1. At a local manufacturing plant, employees must complete new machine setups during a fixed period of time. That time, measured in minutes, can be described by the Normal model N(22, 4). Use your calculator to answer the questions below. Be sure to write out the command you used and the values you entered (no pictures). DO NOT convert these to z-scores and DO NOT complete these questions by hand (no credit will be given if this is done) Round your answers to two decimal places. (3 points each) a. What percent of new machine setups take more than 30 minutes? b. What percent of new machine setups take less than 20 minutes? c. What percent of machine setups take between 24 and 28 minutes? d. Describe the machine setup time for the slowest 5%. e. Describe the machine setup time for the fastest 10%. f. In what interval of machine setup times do the middle 70% fall? 2. Ornithologists (bird specialists) found that, out of the 26 types of penguins, a certain species of penguin has an average height of 65 cm with a standard deviation of 2.5 cm. The scientists collect a random sample of 30 adult penguins and measure their heights. a. Find the mean and standard deviation of the sampling distribution and describe the sampling distribution using the notation N(u, o). (2 points) b. Check all necessary conditions. Provide a full explanation of each condition and how this problem meets them. (2 points) c. What is the probability of a penguin's height being above 66 cm? (2 points) d. What is the probability of the group having an average height above 66 cm? (2 points) e. What is the probability of the group having an average height below 64.3 cm? (2 points)