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.

BanFoxSinOfGreed Apr 29, 2021

#1**+1 **

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

CPhill Apr 30, 2021