The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 4.2 tons. What is probability that a truck will weigh less than 14.3 tons?
A) 0.0062
B) 0.3632
C) 0.1368
D) 0.4938

Question

Quizplus · Accepted Answer

We can use the standard error formula to calculate the z-score and then find the probability using a standard normal distribution table:
SE = σ/√n = 4.2/√49 = 0.6
z = (14.3 - 15.8)/0.6 = -2.5
Using a standard normal distribution table, we find that the probability of a z-score being less than -2.5 is 0.0062, which is the answer choice A.

The Mean Weight of Trucks Traveling on a Particular Section