A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of $187 \mathrm{lb}$ and a standard deviation of $35 \mathrm{lb}$. The water taxi has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of $3500 \mathrm{lb}$. Complete parts (a) through (d) below.
a. Given that the water taxi was rated for a load limit of $3500 \mathrm{lb}$, what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers?
The maximum mean weight is Ib.
(Type an integer or a decimal. Do not round.)
Answer
Final Answer: The maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers is \(\boxed{140}\) lb.
Step 1 ：Given that the water taxi was rated for a load limit of 3500 lb, we need to find the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers.
Step 2 ：We can calculate the maximum mean weight by dividing the total load limit by the number of passengers. The formula for this is \(\frac{load\_limit}{passenger\_capacity}\).
Step 3 ：Substituting the given values into the formula, we get \(\frac{3500}{25} = 140\).
Step 4 ：Final Answer: The maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers is \(\boxed{140}\) lb.
