Answered

Suppose the temperature during the summer has a mean of 90° and a standard deviation of 2°. If each day during the winter the temperature is half the temperature during the summer, what will the winter mean temperature and standard deviation be?

A. mean = 45°, standard deviation = 4°
B. mean = 45°, standard deviation = 2°
C. mean = 45°, standard deviation = 1°



Answer :

GinnyAnswer
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°

Other Questions