An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed, with mean 117 cm and standard deviation 2.1 cm. If three units are selected at random find the probability that exactly two have lengths exceeding 120 cm. ( Round your answer to 4 decimal places)
Solution :
Given that ,
mean = = 117
standard deviation = = 2.1
_{} = / n = 2.1 / 3 = = 1.2124
P( > 120) = 1 - P( < 120)
= 1 - P[( - _{} ) / _{} < (120 - 117) / 1.2124]
= 1 - P(z < 2.47)
= 1 - 0.9932
= 0.0068
Probability= 0.0068
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