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?

Answer 1

Answer:

Given,

Let us assume X be the random variable which denotes the predictor

E(X) = u

Standard deviation =

P(Correct temperature) = P(u + 3​ < X < u + 3​)

= P(-3​ < X - u < 3​)

= P(-3 < z < 3)

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

= 0.9987 - 0.0014 [since from z table]

= 0.9973

So the predictor predicts with accuracy of 99.73%.