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The weight of men in the United States as of 2020 is said to have a mean of 198 lbs with a standard deviation of 15 lbs. Suppose that we take a sample of size 6.

Answer :

Final answer:

To find the probability that 20 randomly selected men will have a sum weight greater than 3,600 pounds, we can use the Central Limit Theorem. Using the mean and standard deviation provided, we can calculate the z-score and use a standard normal table to find the probability. In this case, the probability is practically 0.

Explanation:

To find the probability that 20 randomly selected men will have a sum weight greater than 3,600 pounds, we need to use the Central Limit Theorem since we are dealing with a sample mean. The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. Since the sample size is 20 and assumed to be randomly selected, we can use the normal distribution to find the probability.

First, we need to calculate the mean and standard error of the sample mean. The mean weight of men is given as 198 lbs, so the mean weight of 20 randomly selected men is 198 * 20 = 3960 lbs. The standard deviation of the population is given as 15 lbs, so the standard error of the sample mean is 15 / sqrt(20) = 3.354 lbs.

Next, we need to calculate the z-score, which measures how many standard errors a value is away from the mean. The z-score is calculated as (x - mean) / standard error. In this case, x is the sum weight of 20 randomly selected men, which is 3600 lbs. Using the formula, the z-score is (3600 - 3960) / 3.354 ≈ -10.75.

Finally, we can use a standard normal table or a calculator to find the probability that a z-score is less than -10.75. The probability is extremely close to 0, which means the probability of 20 randomly selected men having a sum weight greater than 3,600 pounds is practically 0.

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Final answer:

To analyze the weight data from a sample of men in the United States, we can calculate the mean, median, mode, and quartiles. These statistics provide insights into the weight distribution and can be compared to the overall population mean and standard deviation.

Explanation:

In statistics, the weight of men in the United States as of 2020 is said to have a mean of 198 lbs with a standard deviation of 15 lbs. By taking a sample of size 6 from this population, we can analyze the data using the given statistics.

To analyze the data, we can calculate the mean, median, mode, and quartiles for this sample. The mean can be calculated as the sum of all the weights divided by the sample size: (weight1 + weight2 + weight3 + weight4 + weight5 + weight6) / 6. The median is the middle value when the data is arranged in ascending order. The mode is the value that appears most frequently in the data. The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.

By calculating these statistics, we can analyze the weight distribution in this sample and make comparisons to the overall population mean and standard deviation.

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