Question 1192499
**1. Define Variables**

* Let X be the weight loss due to diet. 
* Let Y be the weight loss due to exercise.
* Let Z be the total weight loss (Z = X + Y)

**2. Determine the Distribution of Z**

* Since X and Y are both normally distributed, their sum (Z) is also normally distributed.

* **Mean of Z (μz):** 
    * μz = μx + μy 
    * μz = 500 gms + 200 gms = 700 gms

* **Standard Deviation of Z (σz):**
    * Since X and Y are independent, 
        * σz = √(σx² + σy²) 
        * σz = √(2² + 1²) = √5 gms 

**3. Standardize Z**

* To find the probability, we need to standardize Z:
    * Z-score = (Z - μz) / σz

* For a weight loss of 1 kg (1000 gms):
    * Z-score = (1000 gms - 700 gms) / √5 gms 
    * Z-score = 300 / √5 ≈ 134.16

**4. Find the Probability**

* We need to find P(Z ≥ 1000 gms) 
* Since the Z-score is extremely high (134.16), the probability of losing 1 kg or more with both diet and exercise is **extremely close to 1 (or 100%)**. 

**In essence:**

* Combining a strict diet with an exercise regime leads to a significantly high probability of losing at least 1 kg per week. This is due to the combined effects of both methods and their relatively high mean weight loss and low standard deviations.

**Important Note:** 

* This calculation assumes that the weight loss from diet and exercise are completely independent. In reality, there might be some interaction between the two.
* This is a simplified model, and individual results may vary significantly.
* Sustainable and healthy weight loss typically involves a combination of diet, exercise, and other lifestyle factors. 

I hope this helps! Let me know if you have any other questions.