Question

Trucks pass an automatic scale that monitors 2,000 trucks. This population of trucks has an average weight of 20 tons with a standard deviation of 2 tons. If a sample of 50 trucks is taken, what is the probability the sample will have an average weight within one-half ton of the population mean?

a) 0.3821

b) 0.6826

c) 0.4772

d) 0.3413

Answer 1

To find the probability that a sample of 50 trucks will have an average weight within one-half ton of the population mean, we can use the Central Limit Theorem. The probability is approximately 0.6826.

Step-by-step explanation:

To find the probability that a sample of 50 trucks will have an average weight within one-half ton of the population mean, we can use the Central Limit Theorem.

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Since the population mean is 20 tons and the standard deviation is 2 tons, the standard error of the mean can be calculated as 2 / sqrt(50) = 0.2828.

To find the probability of the sample having an average weight within one-half ton of the population mean, we need to find the probability that the sample mean falls between 19.5 and 20.5 tons. Using a standard normal distribution table or a calculator, we find that this probability is approximately 0.6826.