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

Question

Quizplus · Accepted Answer

We can use the central limit theorem because the sample size is sufficiently large (n=100) and the population standard deviation is known.

The z-score for a sample mean of 120.0125 is:

z = (120.0125 - 120) / (0.05 / √100) = 2.5

Using a standard normal distribution table, we can find the probability that a z-score is greater than 2.5 to be approximately 0.0062. Therefore, the probability that Claude's sample has a mean greater than 120.0125 centimetres is 0.0062.

A Carload of Steel Rods Has Arrived at Cybermatic Construction