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For flight planning purposes, what is the generally accepted male weight in winter?

A. 258 lbs
B. 178 lbs
C. 206 lbs
D. 187 lbs

Answer :

Final answer:

To find the probability of 20 men weighing more than 3,600 pounds in total, we calculate the sum mean weight, find the sum standard deviation, compute the z-score, and then use a normal distribution to determine the probability.

Explanation:

To calculate the probability that 20 randomly selected men will have a sum weight greater than 3,600 pounds, given that men have an average weight of 172 pounds with a standard deviation of 29 pounds, we first need to find the mean and standard deviation of the sum of their weights. The mean sum weight for 20 men can be found by multiplying the individual average weight (172 pounds) by 20, which equals 3,440 pounds. The standard deviation for the sum can be found by multiplying the individual standard deviation (29 pounds) by the square root of the sample size, which in this case is √20.

To find the probability, we will use a normal distribution model since the sample size is large. We transform the problem into a z-score calculation to compare it to a standard normal distribution. The z-score can be found using the formula z = (X - μ) / (σ/√ n), where X is the sum we are comparing (3,600 pounds), μ is the mean sum weight, σ is the standard deviation, and n is the sample size. Once we have the z-score, we can use standard normal distribution tables or a calculator to find the probability that the sum weight is greater than X.

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