Final answer:
To find the probability that the total weight exceeds 290kg for 44 randomly selected adult passengers, calculate the z-score for 290kg and use a standard normal distribution table or calculator to find the probability, which will be extremely close to zero.
Step-by-step explanation:
To find the probability that the total weight exceeds 290kg for 44 randomly selected adult passengers, we need to calculate the z-score for 290kg using the given mean and standard deviation. The z-score formula is z = (x - μ) / σ, where x is the value you want to find the z-score for, μ is the mean, and σ is the standard deviation. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability.
Using the given information, the z-score for 290kg can be calculated as z = (290 - 65) / 12 = 171 / 12 = 14.25.
Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to a z-score of 14.25. The probability is extremely close to zero, indicating that the likelihood of the total weight exceeding 290kg is very low.