NORMAL DISTRIBUTION HOMEWORK ASSIGNMENT Resources: A tutorial on the normal distribution is available in the Start here module for our class. Instructions: To earn full credit, use the following two-step process to answer each of the following questions. Step 1: Draw the standard normal curve, draw lines that indicate the relevant upper and/or lower boundaries under the curve, label the 2- and x-value (when appropriate) for each boundary, and shade in the relevant area under the curve. Step 2: Show all computational work and draw a box around the final answer. Example: Assume that a sample of test scores are normally distributed with a mean of 82 and a standard deviation of 4. Find the probability that a single test score falls between 74 and 78. X-82 X=78 X-74 Ville 2=-2 2-1 2=0 * Lee x1 = 74-82-2 4 Zu8 = X-X: 18-82-1 P(74x478) = P(-2424-1) = 15870228 1359 Submission: Submit a single file to Dropbox that includes your hand-written answers numbered and in order. Multiple files/disorganized solutions will not be accepted. Assume that you are managing an e-commerce delivery service that utilizes manual pickers to prepare customer orders for delivery. You figure the average time for an order to be picked is 30 minutes with a standard deviation equal to the square root of the last two digits of your Georgia Southern University student id #. Use this data to answer the following questions. The following four questions require you to calculate probabilities given z-scores (i.e., the number of standard deviations from the mean). (2 points each) 1. What is the probability that the picking time is 1.5 standard deviations below the mean or less? [Hint: P(z S-1.5)=?] 2. What is the probability that the order picking time is 2.5 standard deviations above the mean or more? 3. What is the probability that the order picking time falls between 1.0 standard deviations below the mean and 2.0 standard deviations above the mean? [Hint: P(-1.0 sz s 2.0)=?] 4. What is the probability that the order picking time is within three standard deviations of the mean. (Hint: P(-3 sz 3) =?] 5. What is the probability that the order picking time is greater than the mean? [Hint: P(250) The following four questions require you to calculate probabilities given x-scores (i.e., raw data). (3 points each) 6. What is the probability that the order picking time is 35 minutes or greater? [Hint: P(x 35.0)=?] 7. What is the probability that order picking time is less than 28 minutes? 8. What is the probability that the order picking time falls between 27 and 34 minutes? [Hint: P[27 Sxs34)=?] 9. What is the probability that order picking time falls between 33 and 35 minutes? The following two questions require you to calculate x-values given probabilities. (4 points each) 10. What is the duration of an order picking time for which 95% of all other order picking durations are longer? [Hint: P(x 2 7) = .95] 11. What is the order picking duration for which 80% of all other order picking durations are shorter? 11