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A certain type of automobile battery is known to last an average of 1,180 days with...

A certain type of automobile battery is known to last an average of 1,180 days with a standard deviation of 50 days. If 100 of these batteries are selected, find the following probabilities for the average length of life of the selected batteries. (Round your answers to four decimal places.)

(a) The average is between 1,172 and 1,180.

(b) The average is greater than 1,188.

(c) The average is less than 950.

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Answer #1

Solution es = 1180 6 = 50 n = 100 4x = 1180 a) P(1172<x<1 180) = P(1172-1180 x-ux ( 5 1180-1180) = P(-1.6<2co) = P(zlo) - P(Zb) p() 1188) -|-P (x1188) =1-P ( no 11081180) 1 = 1- P(208) =i-P(z<1.6) = 1 -0.9452 = 0.0548 the average is 0.0548 greater th

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