Question

4. Data (Xi) : 10 12 14 15 17 18 18 24 30 62 71...90

1. Find the Z distribution.

2. Find the Normal probability plot.

3. Conclusions is the Z distribution Skewed.

Answer 1

Solution :

Given,

Data (Xi) : 10 12 14 15 17 18 18 24 30 62 71...90

Given,

(a) Find the Z distribution.

The z distribution is given in the table. [z value corresponding x values] The distribution of z - value is called z - distribution.

The excel picture represents the z - distribution.

The calculation procedure is first we ordered X values, then mention their positions, then calculate

Where i is the position, n is the total number of observations.

Then calculate z values is excel useing the formula {= NORMSINV(fi)}

(b) Find the Normal probability plot.

The picture represents the probability plot or normal probability plot.

(c) Conclusions is the Z distribution Skewed.

The z distribution is skewed because the graph points are not a upward staright line tending points. If all points look like a straight line or most of the points in the straight line.

We can say the normal probability plot represents the data is normal Hence the plot point a straight line.

So it is skewed data.

x	position		z value	x	z value
10	1	0.0206612	-2.04028132	10	-2.0402813
12	2	0.053719	-1.60981607	12	-1.6098161
14	3	0.0867769	-1.36087334	14	-1.3608733
15	4	0.1198347	-1.17581347	15	-1.1758135
17	5	0.1528926	-1.02410618	17	-1.0241062
18	6	0.1859504	-0.89291849	18	-0.8929185
18	7	0.2190083	-0.77554696	18	-0.775547
24	8	0.2520661	-0.66800213	24	-0.6680021
30	9	0.285124	-0.56768639	30	-0.5676864
62	10	0.3181818	-0.47278912	62	-0.4727891
71	11	0.3512397	-0.38197577	71	-0.3819758
72	12	0.3842975	-0.29421314	72	-0.2942131
73	13	0.4173554	-0.20866375	73	-0.2086637
74	14	0.4504132	-0.12461741	74	-0.1246174
75	15	0.4834711	-0.04144373	75	-0.0414437
76	16	0.5165289	0.041443733	76	0.04144373
77	17	0.5495868	0.124617408	77	0.12461741
78	18	0.5826446	0.208663746	78	0.20866375
79	19	0.6157025	0.294213139	79	0.29421314
80	20	0.6487603	0.381975768	80	0.38197577
81	21	0.6818182	0.472789121	81	0.47278912
82	22	0.714876	0.567686391	82	0.56768639
83	23	0.7479339	0.668002132	83	0.66800213
84	24	0.7809917	0.775546958	84	0.77554696
85	25	0.8140496	0.892918486	85	0.89291849
86	26	0.8471074	1.024106184	86	1.02410618
87	27	0.8801653	1.175813473	87	1.17581347
88	28	0.9132231	1.360873343	88	1.36087334
89	29	0.946281	1.609816067	89	1.60981607
90	30	0.9793388	2.040281322	90	2.04028132

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