The last time I asked a question like this I had tried the way they showed me an

Question

The last time I asked a question like this I had tried the way they showed me and even the other person's answers were wrong. My professor will not explain to me clearly how to solve this, could somebody please help me by giving a small explanation?

Potatoes: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 7.5 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 20%. 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 ( u ) =7.5
Standard Deviation ( sd )=0.9
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P ( Z > x ) = 0.2
Value of z to the cumulative probability of 0.2 from normal table is 0.8416
P( x-u/ (s.d) > x - 7.5/0.9) = 0.2
That is, ( x - 7.5/0.9) = 0.8416
--> x = 0.8416 * 0.9+7.5 = 8.2575                  
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 - 7.5/0.9 ) = 0.05
That is, ( x - 7.5/0.9 ) = -1.64
--> x = -1.64 * 0.9 + 7.5 = 6.0196                  
c.
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 - 7.5/0.9 ) = 0.05
That is, ( x - 7.5/0.9 ) = -1.64
--> x = -1.64 * 0.9 + 7.5 = 6.0196                  
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 - 7.5/0.9) = 0.05
That is, ( x - 7.5/0.9) = 1.6449
--> x = 1.6449 * 0.9+7.5 = 8.9804                  

the weights that delineate the middle 90% of Carl's potatoes from is 6.02   to 8.98

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