An army is soliciting proposals for the development of a truck-launched antitank

Question

An army is soliciting proposals for the development of a truck-launched antitank missile. Pentagon officials are requiring that the automatic sighting mechanism be sufficiently reliable to guarantee that 95% of the missiles will fall no more than 50 ft short of their target or no more than 50 ft beyond, what is the largest ? compatible with hat degree of precision? Assume that Y, the horizontal distance a missile travels, is normally distributed with its mean ? equal to the length of the separation between the truck and the target.

Explanation / Answer

I think you want the value of ?

Acc to problem,

P(Y<+50) - P(Y<-50) =0.95.

or, P(Y-<50) - P(Y-<-50) = 0.95

We know, (Y-)/=Z

so, P(Z<50/) - P(Z<-50/)=0.95

or, (50/)-(1-(50/))=0.95

or, 2(50/)=1.95

or, (50/)=0.975

From normal distribution tables,

50/ 1.96

So, =25.51

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