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 to 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 _____________.
A)0.0124
B)0.0062
C)0.4938
D)0.9752
E)1.0000

Question

Quizplus · Accepted Answer

To find the probability that the sample mean is greater than 120.0125 inches, we use the Central Limit Theorem. The standard error (SE) of the sample mean is the population standard deviation divided by the square root of the sample size, which is $0.05 / \sqrt{100} = 0.005$. We then calculate the Z-score for 120.0125 inches, which is $(120.0125 - 120) / 0.005 = 2.5$. Looking up 2.5 on the Z-table gives us the probability of 0.9938 that a Z-score is less than 2.5, so the probability of being greater than 2.5 is $1 - 0.9938 = 0.0062$.

A Carload of Steel Rods Has Arrived at Cybermatic Construction