(4) An electricity company supplies power to consumers in the Eastern region of a country. When the demand for power exceeds the capacity of the cheapest generating station a second station is brought ‘on-line.’ One of the company’s managers makes a daily judgment about the probability that the second station will be required at least once in the following day. The records of his judgments are given below for a period of 600 days.

(a) Plot a calibration curve for the manager and interpret the result.

(b) Calculate the manager’s average Brier score.

(c) Suppose that the manager had simply quoted a probability of 0.5 on all 600 days, what would his Brier score have been?

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Number of days this probability judgment was made Probability assessed by manager 0 0.2 0.5 0.8 1.0 40 160 180 120 100 Number of days second station was used 8 50 110 110 100