Suppose the weights of Farmer Carl\'s potatoes are normally distributed with a m

Question

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8 ounces and a standard deviation of 1.2 ounces.

(a) Carl only wants to sell the best potatoes to his friends and neighbors at the farmer's market. According to weight, this means he wants to sell only those potatoes that are among the heaviest 5%. What is the minimum weight required to be brought to the farmer's market? Round your answer to 2 decimal places.
________ ounces

(b) He wants to use the lightest potatoes as ammunition for his potato launcher but can only spare about 5% of his crop for such frivolities. What is the weight limit for potatoes to be considered for ammunition? Round your answer to 2 decimal places.
_______ounces

(c) Determine the weights that delineate the middle 90% of Carl's potatoes from the others. Round your answers to 2 decimal places.
from_____ to _____ ounces

Explanation / Answer

Mean_wt = mean weight = 8 ounces

Std_Dev_wt = standard deviation of weight = 1.2 ounces

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a) Carl wants the best 5% potatoes (Heaviest) => To calculate the critical value (minimum allowed), we require the z-critical value at 95% level (Z-value tells how far an observed value is away from the mean OR where does the observed value lie in the overall distribution)

Z-critical value(s) are found from Z-table (Link: sixsigmastudyguide.com/wp-content/uploads/2014/04/z-table.jpg)

=> Z-critical for 95% = 1.645 (find 0.95 in table and take corresponding row-column value)

=> Observed value (min. allowed) = mean_wt + Z-critical * (std_dev_wt) = 8 + 1.645*(1.2) = 9.974 [Answer]

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b) Carl wants the worst 5% potatoes (Lightest) => To calculate the critical value (maximum allowed), we require the z-critical value at 5% level (Z-value tells how far an observed value is away from the mean OR where does the observed value lie in the overall distribution)

Z-critical value(s) are found from Z-table (Link: sixsigmastudyguide.com/wp-content/uploads/2014/04/z-table.jpg)

=> Z-critical for 5% = -1.645 (find 0.05 in table and take corresponding row-column value)

=> Observed value (max. allowed) = mean_wt + Z-critical * (std_dev_wt) = 8 - 1.645*(1.2) = 6.026 [Answer]

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From these 2 above exercises, we can find the 90% values in the middle => (5% to 95%) =>

(6.026, 9.974) [Answer]

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