Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 146.3-cm and a standard deviation of 0.5-cm. For shipment, 14 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 146.2-cm and 146.6-cm. P(146.2-cm < M < 146.6-cm) =

Answer 1

Solution :

Given that ,

mean = $\mu$ = 146.3

standard deviation = $\sigma$ = 0.5

P(146.2 < M < 146.6) = P((146.2 - 146.3)/ 0.5) < (M - $\mu$ ) / $\sigma$ < (146.6 - 146.3) / 0.5) )

= P(-0.2 < z < 0.6)

= P(z < 0.6) - P(z < -0.2)

= 0.7257 - 0.4207

= 0.305

P(146.2-cm < M < 146.6-cm) = 0.305