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 (CLT). The probability is approximately 0.237.
Step-by-step explanation:
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 (CLT). According to the CLT, the sum of a large number of independent and identically distributed (i.i.d) random variables will follow a normal distribution. In this case, we can treat the weights of the men as i.i.d random variables with a mean of 172 pounds and a standard deviation of 29 pounds.
The mean weight of 20 men would be 20 * 172 = 3440 pounds. Since we are looking for the probability of the sum weight being greater than 3600 pounds, we need to find the probability that a normally distributed random variable with a mean of 3440 pounds and a standard deviation of sqrt(20) * 29 will be greater than 3600 pounds. Using the standard normal distribution, we can standardize the random variable and find the corresponding z-score.
The z-score can be calculated using the formula z = (x - mean) / standard deviation. In this case, x = 3600 and the mean = 3440, and the standard deviation = sqrt(20) * 29. Calculating the z-score gives us:
z = (3600 - 3440) / (sqrt(20) * 29) = 0.717
Using a standard normal distribution table or a calculator, we can find that the probability of a z-score of 0.717 or greater is approximately 0.237. Therefore, the probability that 20 randomly selected men will have a sum weight greater than 3600 pounds is 0.237.