Question 1193276
**1. Understand the Central Limit Theorem**

* Even though the population of weekly salaries is right-skewed, the Central Limit Theorem states that the distribution of sample means will approach a normal distribution as the sample size increases. 

* **Key Assumptions:**
    * The sample size is sufficiently large (often considered 30 or more).
    * The samples are drawn independently and randomly from the population.

**2. Calculate the Standard Error of the Mean**

* Standard Error (SE) = σ / √n 
    * Where σ is the population standard deviation 
    * And n is the sample size 

**3. Calculate Z-scores**

* To find probabilities related to the sample mean, we need to standardize the values using the z-score formula:
    * z = (x̄ - μ) / SE 
        * Where x̄ is the sample mean
        * μ is the population mean
        * SE is the standard error

**4. Find Probabilities**

* Use a standard normal distribution table or a calculator to find the probabilities associated with the calculated z-scores.

**Important Note:** 

* Since the sample size (n) is not given in the problem, we cannot calculate the exact standard error and z-scores. 
* Therefore, we cannot provide specific numerical probabilities for parts (a) to (c).

**However, we can explain the general approach:**

**a) Between RM900 and RM1100**

* Calculate the z-scores for RM900 and RM1100 using the formula above.
* Find the area under the standard normal curve between these two z-scores. This will give you the probability that the sample mean falls between RM900 and RM1100.

**b) Below RM900**

* Calculate the z-score for RM900.
* Find the area under the standard normal curve to the left of this z-score. This will give you the probability that the sample mean is below RM900.

**c) Greater than RM850**

* Calculate the z-score for RM850.
* Find the area under the standard normal curve to the right of this z-score. This will give you the probability that the sample mean is greater than RM850.

**d) Exactly RM1000**

* The probability of the sample mean being exactly equal to the population mean (RM1000) is **zero**. This is because the normal distribution is continuous, and the probability of any single point on a continuous distribution is zero.

**In summary:**

* The Central Limit Theorem allows us to approximate the distribution of sample means as normal, even when the population is skewed.
* We need to know the sample size (n) to calculate the standard error and determine the specific probabilities.
* The probability of the sample mean being exactly equal to the population mean is always zero for a continuous distribution.

I hope this explanation helps!