Question

An insurance company wants to estimate the average claim amount for motor insurance policies. They take multiple random samples of 50 claims each from a large population. They notice that the distribution of sample means forms a bell-shaped curve , even though the population distribution is right-skewed . Which statistical concept explains this phenomenon?

Q: Answer-An insurance company wants to estimate the average claim amount for motor insurance policies. They...

Explanation The Central Limit Theorem CLT states that, regardless of the shape of the population distribution , the distribution of sample means will tend to be normal bell-shaped if the sample size is sufficiently large typically n 30 . Here, despite the right-skewed nature of the claim amounts , the repeated sampling process ensures that the sample means approximate a normal distribution , allowing for reliable statistical inferences.