Question

View Policies Current Attempt in Progress In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes at 34 kV. The times, in minutes are as follows: 0.30, 0.84,0.99, 1.23,2.74.3.02. 4. 23.4.73,471,6.59.7.26.7.95, 8.16, 12.07.31.62, 32.67.33.86,36.61, and 73.00 Construct a normal probability plot of these data. Does it seem reasonable to assume that breakdown time is normally distributed? Choose the correct answer. Yes, breakdown time is normally distributed No, breakdown time is not normally distributed

Answer 1

Here in this scenario we have to identify whether the given sample is comes from normally distributed population.

To answer this we have to plot the normal probability plot. Normal probability plot is the plot of Standerd normal value against the observation. If we found that the 45° pattern or linear pattern then we can say that the sample is comes from normally distributed population.

To plot the normal probability plot we need following table :

The sample size is n = 19. The following table shows the sample data provided, sorted in ascending order. Also, the theoretical frequencies fi are computed as well as the associated z-scores zi, for i = 1, 2, ..., 19i=1,2,...,19:

Position (i)	X (Asc. Order)	fi	zi
1	0.30	0.0325	-1.846
2	0.84	0.0844	-1.376
3	0.99	0.1364	-1.097
4	1.23	0.1883	-0.884
5	2.74	0.2403	-0.705
6	3.02	0.2922	-0.547
7	4.23	0.3442	-0.401
8	4.71	0.3961	-0.263
9	4.73	0.4481	-0.131
10	6.59	0.5	0
11	7.26	0.5519	0.131
12	7.95	0.6039	0.263
13	8.16	0.6558	0.401
14	12.07	0.7078	0.547
15	31.62	0.7597	0.705
16	32.67	0.8117	0.884
17	33.86	0.8636	1.097
18	36.61	0.9156	1.376
19	73.00	0.9675	1.846

Observe that the theoretical frequencies fi are approximated using the following formula: < fi į – 0.375 n +0.25 where i corresponds to the position in the ordered dataset, and zi is corresponding associated Z-score. This is zi = 0-'(fi) The normal probability plot is obtained by plotting the X-values (your sample data) on the horizontal axis, and the corresponding zi values on your vertical axis. The following normality plot is obtained: Normal Probability Plot o 2.10 1.60 1.10 0.60 0.10 -0. CU -10.61 9.40 19.40 29.40 39.40 49.40 59.40 69.40 79.40 -0.40 -0.90 -1.40 -1.90 -2.40

From the above normal probability plot we can see that the linear pattern which indicates that the sample is in approximately linear trend.

answer,

A) Breakdown times is normally distributed.

Thank you.