The National Forest Service conducted a study of old growth trees in Muir Woods, measuring bark thickness for a sample of 200 old growth redwoods. Sample results are summarized below:

The average thickness for the sample was 7.0 cm. The standard deviation was 1.2 cm. Conduct an appropriate chi square goodness of fit test to test a null hypothesis that bark thickness has a normal distribution. Use the mean sample thickness as your estimate of µ the mean of the normal distribution that you will try to fit to the sample data. Use the sample standard deviation as your estimate of σ, the standard deviation of that normal distribution. Use a 5% level of significance. Compute degrees of freedom as c–3, where c is the number of thickness categories.

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Thickness (centimeters) Frequency numbr 10 36 60 64 20 10 200 under 5-6 67 7-9 8-9 vr Total of trees)