Graded Assignment Unit Test, Part 2: Probability Distributions Answer the questions. When you are finished, submit this test to your teacher for full credit. Total score: ____ of 15 points (Score for Question 1: ___ of 4 points) 1. The number of peanuts in a 16-ounce can of Nut Munchies is normally distributed with a mean of 96.3 and a standard deviation of 2.4 peanuts. The number of peanuts in a 20-ounce can of Gone Nuts is normally distributed with a mean of 112.6 and a standard deviation of 2.8 peanuts. (a) Carmen purchased a 16-ounce can of Nut Munchies and counted 100 peanuts. What is the z-score for this can of peanuts? (b) Angelo purchased a 20-ounce can of Gone Nuts and counted 116 peanuts. What is the z-score for this can of peanuts? (c) Carmen declares that purchasing her can of Nut Munchies with 100 peanuts is less likely than Angelo purchasing a can of Gone Nuts with 116 peanuts. Is Carmen's statement correct? Use the definition of a z-score to support or refute Carmen's claim.

2. Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 4.3. Scores on an aptitude test are normally distributed with a mean of 110 and a standard deviation of 7.1. Boris scored a 57 on the knowledge test and 106 on the aptitude test. Callie scored 63 on the knowledge test and 114 on the aptitude test. (a) Which test did Boris perform better on? Use z-scores to support your answer. (b) Which test did Callie perform better on? Use z-scores to support your answer. (c) Boris also took a logic test. His z-score on that test was 0.93 . Does this change the answer to which test Boris performed better on? Explain your answer using z-scores.

Last year, the numbers of skateboards produced per day at a certain factory were normally distributed with a mean of 20,500 skateboards and a standard deviation of 55 skateboards. (a) On what percent of the days last year did the factory produce 20,555 skateboards or fewer? (b) On what percent of the days last year did the factory produce 20,610 skateboards or more? (c) On what percent of the days last year did the factory produce 20,445 skateboards or fewer?