A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally...

Transcribed Image Text:

A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 183 lb and a standard deviation of 42 lb. The water taxi has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the water taxi was rated for a load limit of 3500 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 140 lb. (Type an integer or a decimal. Do not round.) b. If the water taxi is filled with 25 randomly selected passengers, what is the probability that their mean weight exceeds the value from part (a)? The probability is 1.0000. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the water taxi is filled with 20 randomly selected passengers, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb? The probability is 0.8518 (Round to four decimal places as needed.) A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 183 lb and a standard deviation of 42 lb. The water taxi has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the water taxi was rated for a load limit of 3500 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 140 lb. (Type an integer or a decimal. Do not round.) b. If the water taxi is filled with 25 randomly selected passengers, what is the probability that their mean weight exceeds the value from part (a)? The probability is 1.0000. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the water taxi is filled with 20 randomly selected passengers, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb? The probability is 0.8518 (Round to four decimal places as needed.)