Is this distribution normal A sample of 100 observations was

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

Solution

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