The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last Q.1. Between 7 and 12 months. Q.2. . Less than 7 months Q.3. More than 5 months but less than 10 months

Answer:solvedStep-by-step explanation:Mean = 12 SD = 2 Answer to part 2)  Less than 7 months P(x < 7) P(x < 7) = P(z < (7-12)/2) = P(z < -2.5) This probability can be obtained by referring to the Z table Thus P(x < 7) = 0.00621) Between 7 and 12 monthsP(7 < x < 12) = P( x< 12) - P(x < 7) We have P(x < 12) = 0 ......[because mean = 12] and P(x < 7) = 0.0062 ...[this we got is part a] Thus on plugging these values we get P( 7 < x < 12) = 0.5 - 0.0062 = 0.4938 Thus P(7 < x < 12) = 0.49383