Question

A certain data scientist is testing his predictor (essentially a tool given historical data and would make predictions using said data) that would make predictions about Philadelphia’s temperatures. The predictor produces a correct temperature if the prediction falls within three standard deviations from the target value. Assume that the expected value of each prediction equals the target value. What is the accuracy of the predictor if the distribution of measurements is uniform?

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Answer 1

Answer:

Given,

Let us accept X be the arbitrary variable which signifies the indicator

E(Prediction) = E(X) = u

i.e.,

Target esteem

Standard deviation =

P(Predictor produces a right temperature) = P(Prediction X falls inside 3 standard deviation from the objective worth u)

= P(u + 3​< X < u + 3​)

= P(- 3< X - u < 3​)

= P(- 3 < z < 3)

= P(z < 3) - P(z < - 3)

= 0.9986501 - 0.0013499 [since from z table]

= 0.9987 - 0.0014

= 0.9973

So the indicator predicts with precision of 99.73%.