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3 years ago

What is the estimated margin of error, using standard deviation?

Mathematics

1 answer:

OLEGan [10]3 years ago

3 0

Find the mean ( average):
105 + 104 + 110 + 112 + 114 + 106 + 108 +109 = 868
Mean = 868 / 8 = 108.5

Standard deviation:
108.5 - 105 = 3.5, 3.5^2 = 12.25
108.5 - 104 = 4, 4^2 = 16
110 - 108.5 = 1.5, 1.5^2 = 2.25
112 - 108.5 = 3.5, 3.5^2 = 12.25
114 - 108.5 = 5.5, 5.5^2 = 30.25
108.5 - 106 = 2.5, 2.5^2 = 6.25
108.5 - 108 = 0.5, 0.5^2 = 0.25
109 - 108.5 = 0.5, 0.5^2 = 0.25

12.25 + 16 +2.25 + 12.25 + 30.25 +6.25+0.25+0.25 = 79.75
79.75/8 = 9.96875, SQRT(9.96875) = 3.1573

Standard Deviation = 3.1573

108.8 +/- 1.96 *(3.1573/sqrt(8) = 110.687 and 106.312

110.687 - 108.5 = 2.19
108.5 - 106.312 = 2.19

Margin of error = +/- 2.19

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alina1380 [7]

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Step-by-step explanation:

1. The sum of adjacent angle is 180 degree

115 + 8b +1 = 180

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3 years ago

When the components arrive, the company selects a random sample from the shipment and subjects the selected components to a rigo

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Answer:

(0.059, 0.133)

Step-by-step explanation:

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Proportion of units which failed the test = $\frac{x}{n} = \frac{24}{250} =\frac{12}{125}$ = 0.096

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Confidence level = 95%

z-value for the confidence level = z = 1.96

The true proportion of the components that fail to meet the specification would be:

$(p-z\sqrt{\frac{p \times q}{n}} , p+z\sqrt{\frac{p \times q}{n}})$

Using the values, we get:

$(0.096-1.96 \times \sqrt{\frac{0.096 \times 0.904}{250}} , 0.096+1.96 \times \sqrt{\frac{0.096 \times 0.904}{250}})\\\\ =(0.059,0.133)$

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Answer:

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