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August 5th, 2017, 11:41 PM  #1 
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  Standard and standard deviation
Hello I have 2 questions which i didn't succeed to solve them, I don't even have a direction, so can you help me please? The following given refers to 2 questions  The standard is that the weight of a cheese should be between 94 to 106 grams. 1. The industry produces cheeses, the average of weight is 110 grams, and standard deviation is 8 grams. The percentage of cheeses which don't stand in standard is: a. 77.34% b. 54.68% c. 45.32% d. 22.66% e. None of the answers is correct. 2. The industry produces cheeses, the average of weight is 100 grams. 25% of the cheeses is below the acceptable standard which is 94 grams. The standard deviation is: a. 8.9021 b. 0.674 c. 4.044 d. There aren't enough data for calculate the standard deviation. e. None of the answers is correct. Thanks a lot! 
August 6th, 2017, 12:22 AM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 1,981 Thanks: 1027  Quote:
for (1), the percent of cheese that doesn't fall within standard is 100  the percent of cheese that does fall within standard. The percent of cheese that does fall within standard is $p_{std}=\displaystyle \int_{94}^{106} N_{110,8}(x)~dx = \\ \\ \Phi\left(\dfrac{106110}{8}\right)  \Phi\left(\dfrac{94110}{8}\right) \approx 0.286 = 28.6\%$ $100  28.6 =71.4$ 71.4% doesn't correspond to any of the answers. For (2) $\dfrac{94100}{\sigma} = \Phi^{1}(0.25)$ Use a table or other means to find $\Phi^{1}(0.25)$ and solve the simple algebraic equation for $\sigma$ The answer is one of (a,b,c), I leave it to you to determine which.  
August 6th, 2017, 08:42 AM  #3  
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  Quote:
For (2)  If I understood you, so the answer is c, right? if not, I will try to understand again and will try to find the answer Edit: Wait, I think it's not c, I will try again. Last edited by IlanSherer; August 6th, 2017 at 08:44 AM.  
August 6th, 2017, 08:54 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 1,981 Thanks: 1027  

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