The distance between two points needs to be measured, in meters. The true distance between the points is 10 meters, but due to m

Question

3 years ago

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The distance between two points needs to be measured, in meters. The true distance between the points is 10 meters, but due to m

easurement error we can’t measure the distance exactly. Instead, we will observe a value of 10+???? , where the error ???? is distributed (0,0.04) . Find the probability that the observed distance is within 0.4 meters of the true distance. Give an approximate numerical answer.

Mathematics

1 answer:

luda_lava [24] · Answer 1 · 2022-08-11T22:20:01+03:00

Answer:

The probability that the observed distance is within 0.4 meters is 0.955

Step-by-step explanation:

Margin of error (ME) from the mean can be calculated using the formula

ME=z×s where

z is the corresponding statistic of the probability that the observed distance is within 0.4 meters

s is the standard deviation of the observed error

Error is distributed as N(0,0.04) means that measurements have <em>standard deviation</em> 0.2, square root of 0.04.

<em>Margin of error</em> is given as 0.4 meters.

Thus 0.4=z×0.2 gives z=2 and the corresponding p-value is 0.045, which means that the probability of observing a margin of error 0.4 is 1-0.045=0.955.