SOLUTION: In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 189.8 pounds in the summer,

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Question 1192344: In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 189.8 pounds in the summer, including clothing and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 44.5 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 21 passengers.

What is the approximate probability (±0.001) that the total weight of the passengers exceeds 4375 pounds?
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
**1. Calculate the Mean and Standard Deviation of the Total Weight**
* **Mean:**
* Mean weight of a single passenger = 189.8 pounds
* Mean weight of 21 passengers = 189.8 pounds/passenger * 21 passengers = 3985.8 pounds
* **Standard Deviation:**
* Standard deviation of a single passenger = 44.5 pounds
* Standard deviation of the total weight of 21 passengers = 44.5 pounds/passenger * √21 passengers ≈ 204.4 pounds
**2. Standardize the Total Weight Limit**
* We'll use the z-score to standardize the total weight limit:
z = (Total Weight Limit - Mean Total Weight) / Standard Deviation of Total Weight
z = (4375 pounds - 3985.8 pounds) / 204.4 pounds
z ≈ 1.90
**3. Find the Probability**
* We're interested in the probability that the total weight exceeds 4375 pounds, which corresponds to the area to the right of z = 1.90 under the standard normal distribution curve.
* Using a standard normal distribution table or a calculator, we find:
P(Z > 1.90) ≈ 0.0287
**Therefore, the approximate probability that the total weight of the 21 passengers exceeds 4375 pounds is 0.029.**
**Note:**
* We've used the normal distribution as an approximation, even though passenger weights might not be perfectly normally distributed.
* This approximation should be reasonably accurate due to the Central Limit Theorem, which states that the distribution of the sum or average of a large number of independent random variables tends to be approximately normal, regardless of the underlying distribution of the individual variables.