For a chi-square goodness-of-fit test for a normal distribution using 7 categories with estimated mean and standard deviation, we would use the critical value for 4 degrees of freedom.

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In a chi-square goodness-of-fit test, the degrees of freedom are calculated as the number of categories minus 1 minus the number of parameters estimated from the data. Here, with 7 categories and estimating 2 parameters (mean and standard deviation), the degrees of freedom are 7 - 1 - 2 = 4.

For a Chi-Square Goodness-Of-Fit Test for a Normal Distribution Using