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 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 need to find the probability that the sample mean is greater than 120.0125. We will use the Central Limit Theorem to standardize the sample mean.

The sample mean follows a normal distribution with mean μ = 120 and standard deviation σ/√n = 0.05/√100 = 0.005.

We can standardize the sample mean as follows:

Z = (X̄ - μ) / (σ/√n) = (120.0125 - 120) / (0.005) = 25

The probability of Z being greater than 25 is very small. Looking at the Z-tables, we can see that the probability of Z being greater than 2.5 is approximately 0.0062.

Therefore, the answer is B) 0.0062.

A Carload of Steel Rods Has Arrived at Cybermatic Construction