Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 98.8 cm and a standard deviation of 2.5 cm. For shipment, 22 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 less than 98.7 cm.

Answer 1

Solution :

Given that ,

mean = = 98.8

standard deviation = = 2.5

n = 22

= 98.8

=  / n = 2.5/ 22=0.5330

P( < 98.7) = P[( - ) / < (98.7-98.8) / 0.5330]

= P(z <-0.19 )

Using z table  

= 0.4247

probability=0.4247