manufactured for use in a computer system are specified to have resistances betw
ID: 3063570 • Letter: M
Question
manufactured for use in a computer system are specified to have resistances between 0.13 and 0.15 chms. The actual measured resistances of the wires produced by company A have a normal probability distribution with mean 0,14 ohm and standard deviation 0.005 ohm. (Rand your answers to fur decry pres) (a) What is the probability that a randomly selected wire from company A's production will meet the specifications? (b) If four of these wires are used in each computer system and al are selected from company A, what is the probablity that all four in a randomly selected system will meet the specifications?Explanation / Answer
a) P(0.13 < X < 0.15)
= P((0.13 - mean)/sd < (X - mean)/sd < (0.15 - mean)/sd)
= P((0.13 - 0.14)/0.005 < Z < (0.15 - 0.14)/0.005)
= P(-2 < Z < 2)
= P(Z < 2) - P(Z < -2)
= 0.9772 - 0.0228
= 0.9544
b) P(0.13 < X < 0.15)
= P((0.13 - mean)/(sd/sqrt(n)) < (X - mean)/sd < (0.15 - mean)/(sd/sqrt(n)))
= P((0.13 - 0.14)/(0.005/sqrt(4)) < Z < (0.15 - 0.14)/(0.005/sqrt(4)))
= P(-4 < Z < 4)
= P(Z < 4) - P(Z < -4)
= 1 - 0 = 1
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