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August 5th, 2017, 11:41 PM   #1
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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!
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August 6th, 2017, 12:22 AM   #2
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Quote:
Originally Posted by IlanSherer View Post
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.
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August 6th, 2017, 08:42 AM   #3
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From: Israel

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Quote:
Originally Posted by romsek View Post
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.
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August 6th, 2017, 08:54 AM   #4
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Quote:
Originally Posted by IlanSherer View Post
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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