To find the mean and standard deviation of the number of passengers who do not show up for their flight, we can model the situation using a binomial distribution.
Let:
- \( n = 185 \) (the total number of passengers),
- \( p = 0.0437 \) (the probability that a passenger does not show up).
### Mean
The mean \( \mu \) of a binomial distribution is given by the formula:
\[
\mu = n \cdot p
\]
Substituting the values, we have:
\[
\mu = 185 \cdot 0.0437 = 8.0945
\]
So the mean number of passengers who do not show up is approximately **8.09**.
### Standard Deviation
The standard deviation \( \sigma \) of a binomial distribution is given by the formula:
\[
\sigma = \sqrt{n \cdot p \cdot (1 - p)}
\]
Calculating \( 1 - p \):
\[
1 - p = 1 - 0.0437 = 0.9563
\]
Now substituting the values into the standard deviation formula:
\[
\sigma = \sqrt{185 \cdot 0.0437 \cdot 0.9563}
\]
Calculating this step-by-step:
1. Calculate \( n \cdot p \cdot (1 - p) \):
\[
185 \cdot 0.0437 \cdot 0.9563 \approx 185 \cdot 0.0418 \approx 7.733
\]
2. Now, take the square root:
\[
\sigma \approx \sqrt{7.733} \approx 2.78
\]
### Summary
- **Mean number of passengers who do not show up**: approximately **8.09**
- **Standard deviation of the number of passengers who do not show up**: approximately **2.78**.