Question

g A carload of steel rods has arrived at Cybermatic Construction Company. 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 has a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude's sample has a mean greater than 120.0125 inches is _____________.

Answer 1

0.0062

Explanation:

Given that a carload of steel roads has arrived at Cybermatic Construction Company. The car contains 50,000 rods

Sample size =100

`\bar x=120`

`s =0.05`

Sample mean follows a N(120,0.05/sqrtn)

sample std error=
`(0.05)/(√(100) ) \\=0.005`

`P(\bar X>120.0125)=\\P(Z>(120.0125-120)/(0.005) \\=P(Z>2.5)\\=0.5-0.4938\\=0.0062`