International Baccalaureate (IB) Mathematics Practice Test

The expected frequency for normally distributed data in the goodness-of-fit test is calculated using the formula that involves the probability of each category and the total sample size. By multiplying the probability of an event occurring in a specific category by the total sample size, you derive the expected frequency for that category.

In the case of a goodness-of-fit test, you typically start with theoretical probabilities, which reflect what you would expect to observe if the data followed the assumed distribution (in this case, a normal distribution). When you multiply these probabilities by the total number of observations (or sample size), you can find out how many observations you would expect in each category if the data fits the model well.

This approach provides a systematic way to determine the expected counts for the various categories, which can then be compared to the observed counts to assess how well the data fits the specified distribution.