SOLUTION: Weight loss per week by adopting a particularly restrictive diet is normally distributed with a mean of 500 gms and a standard deviation of 2 gms. Weight loss per week by adopt

Question 1192499: Weight loss per week by adopting a particularly restrictive diet is normally
distributed with a mean of 500 gms and a standard deviation of 2 gms. Weight
loss per week by adopting an exercise regime is normally distributed with
a mean of 200 gms and a standard deviation of 1 gm. What is the probability that
Asha will lose 1kg in 1 week if she adopts both diet and exercise regime?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
**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.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Weight loss per week by adopting a particularly restrictive diet is normally
distributed
with a mean of 500 gms and a standard deviation of 2 gms.
Weight loss per week by adopting an exercise regime is normally distributed with
a mean of 200 gms and a standard deviation of 1 gm.
What is the probability that
Asha will lose 1kg in 1 week if she adopts both diet and exercise regime?
~~~~~~~~~~~~~~~~~~

In this post, calculations by @CPhill are correct, but his final conclusion is FATALLY WRONG.

His conclusion is

        "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%)**.

As I said, this conclusion is FATALLY WRONG.

The correct conclusion is OPPOSITE to it:

        "Since the Z-score is extremely high (134.16), the probability of losing 1 kg or more
        with both diet and exercise is **extremely low and is close to 0 (or 0%)**.

On an intuitive level, it should be clear even to a hedgehog or a rabbit
due to their common sense, without making any calculations.

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