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 cm and a standard deviation of 0.05 cm, the probability that Claude's sample has a mean greater than 120.0125 cm is ___.
A) 0.0124
B) 0.0062
C) 0.4938
D) 0.9752
E) 1.0000

Question

Quizplus · Accepted Answer

We know that the population mean is μ = 120 cm, the sample size is n = 100, the sample mean is x̄ > 120.0125 cm, the population standard deviation is σ = 0.05 cm.

We need to calculate the sample mean standard error (SE):

SE = σ/√n = 0.05/√100 = 0.005 cm

Next, we need to standardize the sample mean using the standard normal distribution:

z = (x̄ - μ) / SE = (120.0125 - 120) / 0.005 = 25

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score greater than 25 is very low, less than 0.01. Therefore, the probability of getting a sample mean greater than 120.0125 cm is also very low.

The closest answer choice is B) 0.0062, which is the best choice.

A Carload of Steel Rods Has Arrived at Cybermatic Construction