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 38 passengers, and a flight has fuel and baggage that allows for a total passenger 6,270 lb load of 6,270 Ib. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 0 = 165 Ib. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 180.6 lb and a standard deviation of 36. The probability is approximately (Round to four decimal places as needed.) Should the pilot take any action to correct for an overloaded aircraft? O A. No. Because the probability is high, the aircraft is safe to fly with its current load. O B. Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![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 38 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,270 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than \( \frac{6,270 \, \text{lb}}{38} = 165 \, \text{lb} \). What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 180.6 lb and a standard deviation of 36.
The probability is approximately [ ].
(Round to four decimal places as needed.)
Should the pilot take any action to correct for an overloaded aircraft?
- ○ A. No. Because the probability is high, the aircraft is safe to fly with its current load.
- ○ B. Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea1b3038-96e6-41c5-a68e-86a6d322f782%2Fa68beef9-4a31-4ea2-a540-893c94d3df78%2Fphed208_processed.png&w=3840&q=75)
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