Question

Trucks pass an automatic scale that monitors 2,000 trucks. This population of trucks has an average weight of 29 tons with a standard deviation of 3 tons. If a sample of 190 trucks is taken, what is the probability the sample will have an average weight within one-half ton of the population mean? (Round your answer to four decimal places.)

Answer 1

To calculate the probability that a sample of 190 trucks will have an average weight within one-half ton of the population mean, use the sampling distribution of the mean and the Z-score formula. The probability of a Z-score being 0 is 0.5.

Step-by-step explanation:

To calculate the probability that a sample of 190 trucks will have an average weight within one-half ton of the population mean, we need to use the sampling distribution of the mean. Since the sample size is larger than 30 and the population standard deviation is known, we can use the normal distribution.

The standard error of the mean is calculated by dividing the standard deviation of the population by the square root of the sample size. In this case, the standard error is 3/√190 ≈ 0.2181.

To find the probability, we can use the Z-score formula: Z = (sample mean - population mean) / standard error. In this case, we want the sample mean to be within one-half ton of the population mean, so we have Z = (29 - 29)/(0.2181) = 0. The probability of a Z-score being 0 is 0.5.