Question

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)

Answer 1

X = length

X follow normal distribution with mean = 117 and sd = 2.1

Z = (X - mean)/sd = (X - 117)/2.1

P(X > 120)

= P(Z > (120 - 117)/2.1)

= P(Z > 1.42857 )

= 0.0766

Y = number of units which have lengths exceeding 120 cm

Y follow binomial distribution with n = 3 , p = 0.0766

P(Y = 2)

= 3C2 * 0.0766^2* (1-0.0766)

= 3* 0.0766^2* (1-0.0766)

= 0.0162543

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