Answer :
Final answer:
To find the probability that the sample average weight of 45 fully-loaded delivery trucks is more than 5780 pounds, we can use the Central Limit Theorem. The probability is approximately 0.1486, or 14.86%.
Explanation:
To find the probability that the sample average weight of 45 fully-loaded delivery trucks is more than 5780 pounds, we can use the Central Limit Theorem. According to the Central Limit Theorem, when the sample size is large enough, the sampling distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution. The mean of the sampling distribution of the sample means is equal to the population mean, which is 5750 pounds in this case. The standard deviation of the sampling distribution of the sample means, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard error is 195 pounds divided by the square root of 45, which is approximately 29.08 pounds. We can then calculate the z-score by subtracting the population mean from the sample mean and dividing the result by the standard error. The z-score represents the number of standard deviations the sample mean is away from the population mean. We can use the z-score to find the probability using a standard normal distribution table or a calculator.
Let's calculate the z-score:
z = (5780 - 5750) / 29.08
z = 1.03
Next, we can look up the probability corresponding to a z-score of 1.03 in a standard normal distribution table or use a calculator. The probability that the sample average weight of 45 fully-loaded delivery trucks is more than 5780 pounds is approximately 0.1486, or 14.86%.
Learn more about Central Limit Theorem here:
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