Is this distribution normal? A sample of 100 observations was taken. You wish to

Question

Is this distribution normal? A sample of 100 observations was taken. You wish to assess whether these observations may have some from a Normal distribution. The sample had y = 100 and s = 10. The number of observations in each bin are given in the following table. The null hypothesis is that the sample did come from a normal distribution with Mu = 100 and sigma = 10. This null hypothesis can be restated in terms of the true proportions of each category, the pi i's.. Give the values of pi1 through pi8 (to 4 decimal places). Hint: pi1 = P(X

Explanation / Answer

H0: The sample did come from a normal distribution.

mu =100 sigma = 10 and n =100

P(X<80) = P(Z<-2) =0.0228

P(80-90) = P(2<z<3) = 0.0225

Thus total prob =1 with 0.02 may be due to rounding off correction.

x <80 80-90 90-95 95-100 100-105 105-110 110-120 >120 Total fre 5 11 13 22 18 16 9 6 100 Prob 0.05 0.11 0.13 0.22 0.18 0.16 0.09 0.06 1 Normal pro 0.0228 0.1459 0.1498 0.1915 0.1915 0.1498 0.1459 0.0228 1.02

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