Passengers died when a particular water taxi sank. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 208 lb and a standard deviation of 45 lb. The water taxi that sank had a stated capacity of 25 passengers, and the boat was rated for a load limit of 4000 lb. Complete parts (a) through (d) below. a. Given that the water taxi that sank was rated for a load limit of 4000 lb, what is the maximum mean weight of the passengers if the boat is filled to the stated capacity of 25 passengers? The maximum mean weight is 160 lb. (Type an integer or a decimal. Do not round.) b. If the water taxi is filled with 25 randomly selected men, 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. After the water taxi sank, the weight assumptions were revised so that the new capacity became 20 passengers. If the water taxi is filled with 20 randomly selected men, what is the probability that their mean weight exceeds 200 lb, which is the maximum mean weight that does not cause the total load to exceed 4000 lb? The probability is (Round to four decimal places as needed.) An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 157 lb and a standard deviation of 27.5 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 191 lb. The probability is approximately 0.4912. (Round to four decimal places as needed.) b. If 38 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 191 lb. The probability is approximately (Round to four decimal places as needed.) Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,216 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean 6,216 lb 168 lb. What is the probability that the aircraft is overloaded? 37 weight of the passengers is greater than Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 180.8 lb and a standard deviation of 35.8. The probability is approximately 0.9850 (Round to four decimal places as needed.) Should the pilot take any action to correct for an overloaded aircraft? A. Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft. B. No. Because the probability is high, the aircraft is safe to fly with its current load. A. According to one study, brain weights of men are normally distributed with a mean of 1.20 kg and a standard deviation of 0.14 kg. Use the data to answer questions (a) through (e). Pop 1.2 n=3 n=12 Ly B. C. Q Pop n=3 n = 12 1.2 LY Pop 1.2 n=12 n=3 d. Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. 78.50% (Round to two decimal places as needed.) e. Determine the percentage of all samples of twelve men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. % (Round to two decimal places as needed.) LV