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prohojiy [21]
3 years ago
5

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a stan

dard deviation of 20. What percentage of the time will the number of boxes of supplies that arrive be greater than 210 or less than 180?
Mathematics
1 answer:
Archy [21]3 years ago
8 0

Answer:

46.72%.

Step-by-step explanation:

We have been given that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. We are asked to find the number of boxes of supplies that arrive will be greater than 210 or less than 180.  

We will use z-score formula and normal distribution table to solve our problem.

z=\frac{x-\mu}{\sigma}

z=\frac{180-200}{20}

z=\frac{-20}{20}

z=-1

Let us find z-score corresponding to normal score 210.

z=\frac{210-200}{20}

z=\frac{10}{20}

z=0.5

P(z0.5)=P(z

Using normal distribution table, we will get:

P(z0.5)=0.15866+1-0.69146

P(z0.5)=0.4672

0.4672\times 100\%=46.72\%

Therefore, 46.72% of the time the number of boxes of supplies that arrive will be greater than 210 or less than 180.

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Answer:

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Step-by-step explanation:

We want to solve this problem using a matrix, so it would be wise to apply Gaussian elimination. Doing so we can start by writing out the matrix of the coefficients, and the solutions ( - 5 and - 2 ) --- ( 1 )

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Row Echelon Form :

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