Potatoes: Suppose the weights of Farmer Carl\'s potatoes are normally distribute

Question

Potatoes: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8 ounces and a standard deviation of 1.1 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 25%. 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 99% of Carl's potatoes from the others. Round your answers to 2 decimal places. from to ounces

Explanation / Answer

a) P(Z > z*) = 0.25

z* = 0.674

X = 8 + 1.1 *0.674 = 8.7414 = 8.74

b) P(z <z*) = 0.05

z* = -1.645

hence

X = 8 -1.645 * 1.1 = 6.1905

= 6.19

c) 99 %

P(Z > z*) = 1-0.99/2 = 0.005

z* = 2.576

hence

lower critical value = 8 -2.576 *1.1 =5.1664 = 5.17

upper critical value = 8 +2.576 *1.1 = 8.7414 = 8.74

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