Not understanding how to do this, please help me Potatoes: Suppose the weights o

Question

Not understanding how to do this, please help me

Potatoes: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8 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 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 95% of Carl's potatoes from the others. Round your answers to 2 decimal places.

____from to ____ounces

Explanation / Answer

a.
Mean ( u ) =8
Standard Deviation ( sd )=0.09
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.05
Value of z to the cumulative probability of 0.05 from normal table is 1.6449
P( x-u/ (s.d) > x - 8/0.09) = 0.05
That is, ( x - 8/0.09) = 1.6449
--> x = 1.6449 * 0.09+8 = 8.148                  
b.
P ( Z < x ) = 0.05
Value of z to the cumulative probability of 0.05 from normal table is -1.645
P( x-u/s.d < x - 8/0.09 ) = 0.05
That is, ( x - 8/0.09 ) = -1.64
--> x = -1.64 * 0.09 + 8 = 7.852                  
c.
P ( Z < x ) = 0.025
Value of z to the cumulative probability of 0.025 from normal table is -1.96
P( x-u/s.d < x - 8/0.09 ) = 0.025
That is, ( x - 8/0.09 ) = -1.96
--> x = -1.96 * 0.09 + 8 = 7.8236                  
P ( Z > x ) = 0.025
Value of z to the cumulative probability of 0.025 from normal table is 1.96
P( x-u/ (s.d) > x - 8/0.09) = 0.025
That is, ( x - 8/0.09) = 1.96
--> x = 1.96 * 0.09+8 = 8.1764                  

95% of Carl's potatoes from the others are 7.8236   from to 8.1764ounces

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