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 9 ounces and a standard deviation of 0.9 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 eight required to be brought to the armer'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 Carls potatoes rom the others. Round your answers to 2 decima from places. to ounces

Explanation / Answer

mean = 9

sd = 0.9

a)

For 5%, z-value = 1.6449 (using standard normal z-table)

Using central limit theorem,

x = mean + z*sd

x = 9 + 1.6449*0.9

x = 10.48

hence 10.48 ounces

b)

For 5%, z-value = -1.6449 (using standard normal z-table)

Using central limit theorem,

x = mean + z*sd

x = 9 - 1.6449*0.9

x = 7.52

hence 7.52 ounces

c)

mean = 9

z-value of 99% CI = 2.5758

std. dev. = 0.9

SE = sd = 0.9

ME = z*SE = 2.31825

Lower Limit = Mean - ME = 6.68175

Upper Limit = Mean + ME = 11.31825

99% CI (6.6818 , 11.3182 )

Hence 6.68 to 11.32 ounces

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