Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 108.7-cm and a standard deviation of 0.6-cm. For shipment, 22 steel rods are bundled together.
Find the probability that the average length of rods in a randomly selected bundle of steel rods is less than 109.1-cm.


Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

Answer 1

Let x be the lengths of the steel rods and X ~ N (108.7, 0.6)

To get the probability of less than 109.1 cm, the solution is computed by:

z (109.1) = (X-mean)/standard dev

= 109.1 – 108/ 0.6

= 1.1/0.6

=1.83333, look this up in the z table.

P(x < 109.1) = P(z < 1.8333) = 0.97 or 97%