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?Solution
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.
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