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 between 119.985 and 120.0125 cm is ___.
A) 0.9925
B) 0.9974
C) 0.9876
D) 0.9544
E) 0.9044

Question

Quizplus · Accepted Answer

The probability that Claude's sample has a mean between 119.985 and 120.0125 cm is 0.9925. This is because the sample mean is normally distributed with a mean of 120 cm and a standard deviation of 0.05 cm / sqrt(100) = 0.005 cm. The probability that the sample mean is between 119.985 and 120.0125 cm is the area under the normal curve between these two values, which is 0.9925.

A Carload of Steel Rods Has Arrived at Cybermatic Construction