The weight of trucks traveling on a particular section of I-475 has a population mean of 15.8 tons and a population standard deviation of 4.2 tons. What is the probability a state highway inspector could select a sample of 49 trucks and find the sample mean to be 14.3 tons or less?
A)0.0062
B)0.3632
C)0.1368
D)0.4938

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the Central Limit Theorem (CLT) since we are dealing with a sample mean. According to the CLT, the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case:

mean = 15.8 tons
standard deviation = 4.2 tons / sqrt(49) = 0.6 tons
sample mean = 14.3 tons

To find the probability of selecting a sample of 49 trucks and finding a sample mean of 14.3 tons or less, we need to standardize the sample mean using the formula:

z = (x - mean) / standard deviation

where x is the sample mean. Thus,

z = (14.3 - 15.8) / 0.6 = -2.5

Using a standard normal distribution table, we can find the probability that a z-score is less than or equal to -2.5, which is 0.0062. Therefore, the probability of selecting a sample of 49 trucks and finding a sample mean of 14.3 tons or less is 0.0062, which corresponds to choice A.

The Weight of Trucks Traveling on a Particular Section of I-475