Question

Given that the gondola is rated for a load limit of 3500lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is Ib. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is (Round to four decimal places as needed.) lb, which is the maximum mean weight that does not cause the total load to exceed 3500lb ? The probability is (Round to four decimal places as needed.) d. Is the new capacity of 20 passengers safe? Since the probability of overloading is the new capacity to be safe enough.

Answer 1

The maximum mean weight per passenger for the gondola is 140 lb. Calculating the probability that the mean weight exceeds this requires additional data. For 20 passengers, the load limit increases to 175 lb per person, potentially indicating safety for average weights under normal conditions.

Step-by-step explanation:

To find the maximum mean weight of the passengers that the gondola can carry when filled to its stated capacity of 25 passengers, we need to divide the total load limit by the number of passengers. Therefore, the maximum mean weight per passenger is 3500 lb ÷ 25 passengers = 140 lb per passenger.

For part b, to calculate the probability that the mean weight of 25 randomly selected passengers exceeds 140 lb, we would need the population standard deviation and to assume that the weights are normally distributed. Given those, one could use standard scoring and the normal distribution table to find this probability. However, since the needed information is not provided, we cannot compute the probability.

Regarding part b question about the safety concern for 20 men, we would consider if the sum of their weights exceeds the load limit. Since the per-person load limit with 25 passengers is 140 lb and for 20 passengers it would be 3500 lb ÷ 20 = 175 lb per person, 20 men would have to each weigh less than 175 lb to be within safety limits. If they all weigh more, it could be a safety concern.

For part d, a new capacity of 20 passengers allows for a higher mean weight per person (175 lb each). Considering typical adult male weights and assuming they are not carrying extra heavy equipment, this could be regarded as safe. However, without knowing the actual distribution of passenger weights, no definitive conclusion can be drawn about the safety.