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Asked Dec 9, 2019
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2. A manufacturing process produces items whose weights are normally distributed. It is known that
22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the
mean up to 190 grams. Determine the mean and the standard deviation.
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2. A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

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Expert Answer

Step 1

2.

You use z=(x-mu)/sigma twice and get two linear equations which you can then solve for µ and σ.
One equation: 0.2257 units of area between z and 0, so 0.5000 – 0.2257 = 0.2743 area to the left of z. Use a table of values or a stats calculator to find z= –0.6 approximately. Substitute z= –0.6 and x=100 into z=(x-mu)/sigma.

Second equation: area 0.4918 from mean (z=0) to 190. Area to left is 0.5+0.4918 = 0.9918 which gives a z value of z=2.4 approximately. Substitute z=2.4, x=190 into z=(x-mu)/sigma.

Two equations in two unknowns , use linear algebra to solve:

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(100– 4) (1) -0.6 = (190 – u) (2) 2.4 = [:(1)×(2)] 3(0) = 90 90 3 O = 30

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Step 2

The value of m...

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u =100+0.6(0) =100 +0.6(30) =100 +18 =118

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