To find the new mean and standard deviation after increasing each drop time by 1.5 seconds, let's break down the process step-by-step.
1. Initial Mean and Standard Deviation:
- The initial mean time for drops from a height of 25 feet is 4.2 seconds.
- The standard deviation of the drop times is 0.5 seconds.
2. Effect on Mean:
- When we increase each drop time by a constant value (in this case, 1.5 seconds), the new mean can be found by adding this constant value to the initial mean.
- Therefore, the new mean is:
[tex]\[
\text{New Mean} = \text{Initial Mean} + \text{Increase}
\][/tex]
Substituting the values:
[tex]\[
\text{New Mean} = 4.2 \text{ seconds} + 1.5 \text{ seconds} = 5.7 \text{ seconds}
\][/tex]
3. Effect on Standard Deviation:
- The standard deviation measures the spread or variability of the data points around the mean. When a constant value is added to each data point, the spread of the data does not change, therefore, the standard deviation remains the same.
- Hence, the new standard deviation is:
[tex]\[
\text{New Standard Deviation} = 0.5 \text{ seconds}
\][/tex]
Based on these calculations, the new mean time for drops from a height of 35 feet is 5.7 seconds, and the standard deviation remains unchanged at 0.5 seconds.
So, the correct answer is:
- Mean: 5.7 seconds
- Standard Deviation: 0.5 seconds
