Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 174 cm and a standard deviation of 1.2 cm.  

Find the proportion of steel rods with lengths between 170.6 cm and 172.4 cm. Round to 4 decimal places.

Answer 1

Solution :

Given that,

mean = = 174

standard deviation = = 1.2

P (311 < x < 331 )

P ( 170.6 - 174 / 1.2 ) < ( x -  / ) < ( 172.4 - 174 / 1.2)

P ( - 3.4 / 1.2 < z < -1.6 /1.2 )

P (-2.83 < z < -1.33 )

P ( z < -1.33 ) - P ( z < -2.83 )

Using z table

= 0.0918 - 0.0023

= 0.0895

Probability = 0.0895