Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 255.9 cm and a standard deviation of 0.9 cm. For shipment, 23 steel rods are bundled together.

Note: Even though our sample size is less than 30, we can use the z score because
1) The population is normally distributed and
2) We know the population standard deviation, sigma.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 256 cm.


Enter your answer as a number accurate to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 255.9

standard deviation = =0.9

n = 23

The population is normally distributed

= 255.9

=  / n = 0.9 / 23=0.18766

P( <256 ) = P[( - ) / < (256 -255.9) / 0.18766]

= P(z <0.53 )

Using z table  

=0.7019

probability=0.7019