A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 92.6-cm and a standard deviation of 2-cm. For shipment, 12 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm. Enter your answer as a number accurate to 4 decimal places.

Answer: 0.2140Step-by-step explanation:Given : A company produces steel rods. The lengths of the steel rods are normally distributed with [tex]\mu=92.6 \text{ cm}[/tex][tex]\sigma=2\text{ cm}[/tex]Sample size : [tex]n=12[/tex]Let x be the length of randomly selected item.z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]For x=92 cm[tex]z=\dfrac{92-92.6}{\dfrac{2}{\sqrt{12}}}\approx-1.04[/tex]For x=92.4 cm[tex]z=\dfrac{92.4-92.6}{\dfrac{2}{\sqrt{12}}}\approx-0.35[/tex]The probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm by using the standard normal distribution table = [tex]P(92<x<92.4)=P(-1.04<z<-0.35)=P(z<-0.35)-P(z<-1.04)[/tex][tex]= 0.3631693-0.14917=0.2139993\approx0.2140[/tex]Hence, the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm is 0.2140.