A sample of n captured Pandemonium jet fighters results in serial numbers x 1 ,

Question

A sample of n captured Pandemonium jet fighters results in serial numbers x1, x2, x3, . . . , xn. The CIA knows that the aircraft were numbered consecutively at the factory starting with and ending with , so that the total number of planes manufactured is + 1 (e.g., if = 17 and = 29, then 29 17 + 1 = 13 planes having serial numbers 17, 18, 19, . . . , 28, 29 were manufactured.) However, the CIA does not know the values of or . A CIA statistician suggests using the estimator max(Xi) min(Xi) + 1 to estimate the total number of planes manufactured.

(a) If n = 5, x1 = 483, x2 = 486, x3 = 530, x4 = 591, and x5 = 237, what is the corresponding estimate?

Explanation / Answer

Maximum of X (X4)=591

Minimum of X (X5) =237

correspondig estimate = Max(xn)-Min(xn)+1 = 591-237+1 = 355

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