My Math Forum Standard and standard deviation

 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
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Quote:
 Originally Posted by IlanSherer 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. !
Let $\Phi(x)$ be the CDF of the standard normal distribution

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

$p_{std}=\displaystyle \int_{94}^{106} N_{110,8}(x)~dx = \\ \\ \Phi\left(\dfrac{106-110}{8}\right) - \Phi\left(\dfrac{94-110}{8}\right) \approx 0.286 = 28.6\%$

$100 - 28.6 =71.4$

71.4% doesn't correspond to any of the answers.

For (2)

$\dfrac{94-100}{\sigma} = \Phi^{-1}(0.25)$

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
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Quote:
 Originally Posted by romsek Let $\Phi(x)$ be the CDF of the standard normal distribution 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 $p_{std}=\displaystyle \int_{94}^{106} N_{110,8}(x)~dx = \\ \\ \Phi\left(\dfrac{106-110}{8}\right) - \Phi\left(\dfrac{94-110}{8}\right) \approx 0.286 = 28.6\%$ $100 - 28.6 =71.4$ 71.4% doesn't correspond to any of the answers. For (2) $\dfrac{94-100}{\sigma} = \Phi^{-1}(0.25)$ 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.
For (1) - Thanks!
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
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Quote:
 Originally Posted by IlanSherer For (1) - Thanks! 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.
it's not (c)

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