Question

In: Statistics and Probability

A motorist goes for a drive, keeping the reading on the speedometer at a constant value...

A motorist goes for a drive, keeping the reading on the speedometer at a constant value of 40 km/h. The speedometer is assumed to be accurate to +- 2 km/h. At the end of the day he wants to know how far he has travelled, but unfortunately he forgot to look at the distance indicator when he set out. He thinks that he drove for four hours, give or take a quarter of an hour. Estimate how far he travelled and assign an error to your result.

Expert Solution

Suppose, random variable T denotes time of driving (in hours) and S denotes speed (in km/hour).

So, random variable X denoting travel distance (in km) is given by .

Clearly,

Since, time of driving and speed of driving are independent.

So, estimated distance he travelled is

Minimum value of S is given by

Minimum value of T is given by

Minimum value of X is given by

Maximum value of S is given by

Maximum value of T is given by

Maximum value of X is given by

So, true value of distance travelled is in the interval .

So, possible amount of error is given by

Hence, estimated value of distance travelled is 160 km and maximum possible error to the result is 18.5 km.

orchestra answered 1 year ago

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