Question

Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes a)

(6 pts) What is the mean and variance of the time it takes an operator to fill out the form?

b) (6 pts) What is the probability that it will take less than two minutes to fill out the form?

c) (6 pts) Determine the value for x such that ?(? < ?) = 0.9

. d) (7 pts) Determine the cumulative distribution function of the time it takes to fill out the form.

Answer 1

sol! Given that, Xn u 41.5, 2.2) = XNu (a, b) f here Anti5 b = 2.2. Pidifof uniform distributten is gives beye Flas bra it acxcb otherwise 7 Means of uniform distribution = Mean 2.2+1,5 bta 2 2 (b-q)2 Mean = 1-85 AM Variance of uniform listribution Variance (2-2-1:5) 12 0.49 12 12 Variance 0·04 08 An 2 (6) P(X<2) .doc .. dae 1.5 (2.2-1.5) ota 4241.5) 07 Falls 0.7 P(X22) 0.5 0.7 0.7143 Ay PEX_X) = 0.9 then find a? I tomas ..dae = o.g 1.5 da Dog CS Scammed CamScanner 2.2-1.5) 1-5

X th 0.9 07. [X] 1.5 12–1:5) = 0.9 0. > py 2-1.5 = 0.63 aca 0.63 +1.5 2= Ay 2:13 (d) Cursulative distribution function is: oi xca of uniform dista a < x <b Flau x-a bra 1 27b So o X-1.5 0.7 x L 1.5 152362.2 1 Ay. X7 2.2 Scanned with . CamScanner