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Statistics / Introduction to Probability 1 / Chapter 5 / Problem 24

Introduction to Probability | 1st Edition | ISBN: 9781466575578 | Authors: Joseph K. Blitzstein, Jessica Hwang

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The distance between two points needs to be measured, in meters. The true distance

Chapter 5, Problem 24

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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 cant measure the distance exactly. Instead, we will observe a value of 10+, where the error is distributed N (0, 0.04). Find the probability that the observed distance is within 0.4 meters of the true distance (10 meters). Give both an exact answer in terms of and an approximate numerical answer.

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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 cant measure the distance exactly. Instead, we will observe a value of 10+, where the error is distributed N (0, 0.04). Find the probability that the observed distance is within 0.4 meters of the true distance (10 meters). Give both an exact answer in terms of and an approximate numerical answer.

ANSWER:

Step 1 of 2

Given data:

The true distance between the paints is 10 meters.

We observe a value of normally N(0,0.04).

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