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 9 ounces and a standard deviation of 0.9 ounces.

(a) Carl 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?_________ounces

(c) Determine the weights that delineate the middle 95% of Carl's potatoes from the others. from_______ to_______ ounces

Explanation / Answer

Mean is 9 and s is 0.9

a) this implies we are looking for a value that is 0.75 above the lowest value. form normal distribution table this corresponds to the z value of 0.68. thus x=mean+z*s =9+0.9*0.68=9.612

b) We now need to find the value at 0.05 from bottom most value. this will correspond to z value for 1-0.05=0.95 but with a negative sign. thus it is -1.65 , thus answer is 9-1.65*0.9=7.515

c) for 95% confidence, the z value is 1.96

thus lower limit is 7-1.96*0.9=5.236

upper limit is 8.764

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.