MATHEMATICS HIGH SCHOOL

A chocolate factory produces mints that weigh 10 grams apiece. The standard deviation of the weight of a box of 10 mints is 3 grams. You buy a box of mints that weighs 95 grams. What is your confidence that the box you bought did not come from the factory?A 90%
B 95%
C 10%
D 5%

Answers

Answer 1
Answer:

Answer:  Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Population Mean weight (\mu)= 10 grams a piece

Standard deviation of the weight of a box = 3 grams

Number of mints = 10

We need to buy a box of mints that weighs 95 grams.

Sample mean is given by

x=(95)/(10)=9.5\ grams

First we find out the standard error which is given by

s=(\sigma)/(√(n))\n\n=(3)/(√(10))\n\n=0.94868

Since it is normal distribution, so, we will find z-score.

z=(x-\mu)/(s)\n\nz=(9.5-10)/(0.94868)\n\nz=-0.527\n\nz=-0.53

The area to the left of a z-score of -0.53 = 0.29805.

So, it may be 90% or 95 % confidence.

For 95% confidence level,

\alpha=(1-0.95)/(2)=0.025

Similarly,

For 90% confidence level,

\alpha=(1-0.90)/(2)=0.05

We have little confidence that the box he bought did not come from the factory. that is much smaller than 0.05.

So, it is safe to assume 90% confidence.

So, we will get 90% confidence, critical value = 1.645

Margin of error is given by

(Standard\ deviation)* (critical\ value)\n\n=0.94868* 1.645\n\n=1.56

So, confidence interval will be

(10-1.56,10+1.56)

=(8.44,11.56)

Hence, Option 'A' is correct.
Answer 2
Answer: The right answer for the question that is being asked and shown above is that: "C 10%." A chocolate factory produces mints that weigh 10 grams apiece. The standard deviation of the weight of a box of 10 mints is 3 grams. You buy a box of mints that weighs 95 grams. 

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Answers

Answer:

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Step-by-step explanation:

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3x -  5y = 10     (2)

The easiest way to do this is to multiply Equation (1) by 5

and Equation (2) by 3.

5 × [2x + 3y =  -1]

3 × [3x  - 5y = 10]

Then, add the two equations.

10x + 15y =  -5

9x  - 15y = 30

19x          = 25

Conclusion: Multiply 2x + 3y = −1 by 5. Multiply 3x − 5y = 10 by 3. Add the resulting equations together.

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Answers

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