Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 226.6-cm and a standard deviation of 1.7-cm. For shipment, 10 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is less than 227.9-cm. P(M < 227.9-cm) =

Answer 1

Solution :

Given that,

mean = = 226.6

standard deviation = = 1.7

n = 10

= 226.6

  =  ( /n) = (1.7 / 10 ) = 0.5375

P(M < 227.9)

P ( M -  / ) < ( 227.9 - 226.6 / 0.5375)

P ( z < 1.3 / 0.5375 )

P ( z < 2.42 )

Using z table

= 0.9922

Probability = 0.9922