Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores. Multiply probability by 100 to get percentage.
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.
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 %.
Carl calculates the z-score corresponding to the weight 191 oz. (to the nearest tenth).
Using the table below, Carl sees the percentage associated with this z-score is %
Adding these together, Carl sees the percentage between 169 oz. and 191 oz. is %.
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