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 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 closest to _____________.
A)0.9974
B)0.0026
C)0.4987
D)0.0013
E)0.0030

Question

Quizplus · Accepted Answer

To find the probability that the sample mean is less than 119.985 inches, we use the formula for the z-score of a sample mean: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{119.985 - 120}{0.05/\sqrt{100}} = \frac{-0.015}{0.005} = -3$. Looking up a z-score of -3 in the standard normal distribution table gives a probability of approximately 0.0013.

A Carload of Steel Rods Has Arrived at Cybermatic Construction