The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. If the population of rods have a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude's sample has a mean less than 119.985 inches is A) 0.9974 B) 0.0026 C) 0.4987 D) 0.0013 E) 0.0030

Answer: D) 0.0013Step-by-step explanation:Let x be the random variable that represents the lengths of rods.As pr given , we haven=100 , [tex]\mu=120\ inches[/tex]  [tex]\sigma=0.05\ inch[/tex]z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]For x= 119.985 inches , we have [tex]z=\dfrac{119.985 -120}{\dfrac{0.05}{\sqrt{100}}}=-3[/tex]Using the standard z-table , we haveThe probability that Claude's sample has a mean less than 119.985 inches is [tex]P(z<-3)=1-P(z<3)\\\\=1-0.9986501\\\\=0.0013499\approx0.0013[/tex]Hence, the probability that Claude's sample has a mean less than 119.985 inches is 0.0013.