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 between 119.985 and 120.0125 inches is closest to ____________.
A)0.9925
B)0.9974
C)0.9876
D)0.9544
E)0.9044

Question

Quizplus · Accepted Answer

By the Central Limit Theorem, the sample mean will be approximately normally distributed with a mean of 120 and a standard deviation of 0.05/sqrt(100) = 0.005. So, the probability that the sample mean is between 119.985 and 120.0125 is approximately P(119.985 < X < 120.0125) = P((119.985 - 120)/0.005 < Z < (120.0125 - 120)/0.005) = P(-3 < Z < 5) = 0.9999 - 0.0001 = 0.9998.

A Carload of Steel Rods Has Arrived at Cybermatic Construction