To determine the winter mean temperature and its standard deviation, follow these steps:
1. Given Information:
- Summer mean temperature: 90°
- Summer standard deviation: 2°
2. Winter Mean Temperature Calculation:
- Since the temperature during winter is half of the summer temperature, the winter mean temperature can be found by halving the summer mean temperature.
[tex]\[
\text{Winter mean} = \frac{\text{Summer mean}}{2} = \frac{90°}{2} = 45°
\][/tex]
3. Winter Standard Deviation Calculation:
- The winter temperature's standard deviation will also be half of the summer standard deviation because standard deviation scales linearly with the scaling of the dataset.
[tex]\[
\text{Winter standard deviation} = \frac{\text{Summer standard deviation}}{2} = \frac{2°}{2} = 1°
\][/tex]
4. Conclusion:
- The mean temperature during winter is 45°.
- The standard deviation during winter is 1°.
Thus, the correct values of the winter mean temperature and standard deviation are:
- Mean = 45°
- Standard deviation = 1°
Therefore, the correct option is:
- mean 45°, standard deviation 1°
