Question

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

Answer 1

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 standard deviation 0.2, square root of 0.04.

Margin of error 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.