Non parametric methods, statistics homework help

You are provided with the following summary from a random sample of 127 continuous measurements. Interval: 0 ≤ x < 1, 4 measurements, 1 ≤ x < 2, 14 measurements 2 ≤ x < 3, 38 measurements 3 ≤ x < 4, 42 measurements 4 ≤ x < 5 23 measurements and 5 ≤ x < 6, 6 measurements. By using R, answer: (a) To the extent possible with the data provided, use the Kolmogorov test to assess the null hypothesis that the sample is from a Normal distribution with mean 3.5 and standard deviation 1. (b) Test the same hypothesis with a chi-squared goodness of fit test. (c) What would be the consequences for each of the above approaches if the parameters of the Normal distribution given in (a) had been estimated from the data rather than known a priori? Do the conclusions change?

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