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The number of peanuts in a 16-ounce can of Nut Munchies is normally distributed with a mean of 93.6 and a standard deviation of 4.2 peanuts. The number of peanuts in a 20-ounce can of Gone Nuts is normally distributed with a mean of 111.8 and a standard deviation of 3.4 peanuts.

Part A.

Carmen purchased a 16-ounce can of Nut Munchies and counted 100 peanuts.

What is the -score for this can of peanuts?

Part B

Angelo purchased a 20-ounce can of Gone Nuts and counted 116 peanuts.

What is the score for this can of peanuts?

Part 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.

Apr 29, 2021

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Part A.

Carmen purchased a 16-ounce can of Nut Munchies and counted 100 peanuts.

What is the z-score for this can of peanuts?

(100 -  93.6)  /   4.2   =  1,52        translates  to  .9357

Part B

Angelo purchased a 20-ounce can of Gone Nuts and counted 116 peanuts.

What is the z-score for this can of peanuts?

(116 - 111.8 )  / 3.4   =  1.23       translates  to   .8907

Part 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

What we  can say  is  that  purchasing  a can of Nut Munchies with  less than  100  peanuts  is  more likely  than purchasing a can of Gone Nuts  with less  than 116 peanuts

Apr 30, 2021