Linda keeps track of the time it takes her to drive to work. Over 4 days, she takes 45 minutes, 47 minutes, 41 minutes, and 69 minutes. Without including the outlier, calculate the mean and standard deviation for her travel times. Select one: $$ M=44.3 $$ minutes; $$ S D=2.5 $$ minutes $$ M=42 $$ minutes; $$ S D=2 $$ minutes $$ M=45 $$ minutes; $$ S D=2.5 $$ minutes $$ M=43 $$ minutes; $$ S D=3.5 $$ minutes

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To calculate the mean and standard deviation of Linda's travel times without including the outlier, we first need to identify the outlier among the times: 45 minutes, 47 minutes, 41 minutes, and 69 minutes.

1. **Identify the outlier:**
   - The times are: 45, 47, 41, and 69.
   - The value 69 is significantly higher than the others, so it will be considered the outlier.

2. **Remove the outlier:**
   - The remaining times are: 45, 47, and 41.

3. **Calculate the mean (M):**
   $$
   M = \frac{(45 + 47 + 41)}{3}
   $$

4. **Calculate the standard deviation (SD):**
   - First, we need to find the variance.
   - The formula for variance is:
   $$
   \text{Variance} = \frac{\sum (x_i - M)^2}{n}
   $$
   where $$ x_i $$ are the values, $$ M $$ is the mean, and $$ n $$ is the number of values.

Now, let's perform the calculations step by step.

### Step 1: Calculate the Mean
$$
M = \frac{(45 + 47 + 41)}{3} = \frac{133}{3} \approx 44.33 \text{ minutes}
$$

### Step 2: Calculate the Variance
- Calculate each deviation from the mean:
  - $$ 45 - 44.33 \approx 0.67 $$
  - $$ 47 - 44.33 \approx 2.67 $$
  - $$ 41 - 44.33 \approx -3.33 $$

- Square each deviation:
  - $$ (0.67)^2 \approx 0.4489 $$
  - $$ (2.67)^2 \approx 7.1289 $$
  - $$ (-3.33)^2 \approx 11.0889 $$

- Sum the squared deviations:
$$
0.4489 + 7.1289 + 11.0889 \approx 18.6667
$$

- Calculate the variance:
$$
\text{Variance} = \frac{18.6667}{3} \approx 6.2222
$$

### Step 3: Calculate the Standard Deviation
$$
SD = \sqrt{6.2222} \approx 2.49 \text{ minutes}
$$

### Final Results
- Mean $$ M \approx 44.33 $$ minutes
- Standard Deviation $$ SD \approx 2.49 $$ minutes

Now, rounding the mean and standard deviation to one decimal place gives us:
- $$ M \approx 44.3 $$ minutes
- $$ SD \approx 2.5 $$ minutes

Thus, the correct answer is:
$$ M=44.3 $$ minutes; $$ S D=2.5 $$ minutes.
The mean travel time is approximately 44.3 minutes, and the standard deviation is approximately 2.5 minutes.

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