Weights of the vegetables in a field are normally distributed. From a sample Carl Cornfield determines the mean weight of a box of vegetables to be 180 oz. with a standard deviation of 8 oz. He wonders what percent of the vegetable boxes he has grouped for sale will have a weight between 169 oz. and 191 oz. Carl decides to answer the following questions about the population of vegetables from these sample statistics. You will use some answers more than once. Carl calculates the z-score corresponding to the weight 169 oz. (to the nearest tenth). Using the table, Carl sees the percentage associated with this z-score is

Question

Meghan Maddox

Mathematics

7 December, 00:52

Weights of the vegetables in a field are normally distributed. From a sample Carl Cornfield determines the mean weight of a box of vegetables to be 180 oz. with a standard deviation of 8 oz. He wonders what percent of the vegetable boxes he has grouped for sale will have a weight between 169 oz. and 191 oz. Carl decides to answer the following questions about the population of vegetables from these sample statistics. You will use some answers more than once. Carl calculates the z-score corresponding to the weight 169 oz. (to the nearest tenth). Using the table, Carl sees the percentage associated with this z-score is

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Emely Walsh · Answer 1

For the answer to the question above asking what percent of the vegetable boxes he has grouped for sale will have a weight between 169 oz. and 191 oz. Carl decides to answer the following questions about the population of vegetables from these sample statistics?

P (x > 196) = ?

z = (196 - 180) / 8 = 2

P (x > 196) = P (z > 2) = 0.0228 = 2.3%