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 41 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,724 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 6,724 Ib = 164 lb. What is the probability that the aircraft is overloaded? Should the 41 pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 183.9 lb and a standard deviation of 37.6. 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. OB. Yes. Because the probability is high, the pilot should fake action by somehow reducing the weight of the aircraft.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**Flight Load Verification Problem**

**Scenario:**
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 41 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,724 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:

\[
\frac{6,724 \, \text{lb}}{41} = 164 \, \text{lb}
\]

**Question:**
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 183.9 lb and a standard deviation of 37.6 lb.

**Calculation:**
The probability is approximately:

\[ \text{(Round to four decimal places as needed.)} \]

**Decision:**
Should the pilot take any action to correct for an overloaded aircraft?

- **Option A:** No. Because the probability is high, the aircraft is safe to fly with its current load.
- **Option B:** Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft.
Transcribed Image Text:**Flight Load Verification Problem** **Scenario:** 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 41 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,724 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: \[ \frac{6,724 \, \text{lb}}{41} = 164 \, \text{lb} \] **Question:** 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 183.9 lb and a standard deviation of 37.6 lb. **Calculation:** The probability is approximately: \[ \text{(Round to four decimal places as needed.)} \] **Decision:** Should the pilot take any action to correct for an overloaded aircraft? - **Option A:** No. Because the probability is high, the aircraft is safe to fly with its current load. - **Option B:** Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft.
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