1. On average, 1.5 error per page was found in an exemplary book. What is the probability of finding no more than 1 error on a page in the book.
2. The following data were taken from a study of red-blood-cell counts before and after major surgery. Counts were taken on 23 female patients who had the same blood type (O+).
Patient 1 2 3 4 5 6 7 8 9 1
0 1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 1
2 2
2 3 Pre-op 1
4 1
3 4 5 1
8 3 6 1
1 3
3 1
1 3 3 5 4 1
5 4 0 7 2 8 4 4 5
Post-
op 0 2
6 2 4 8 1 0 3 2
3 2 2 2 6 0 3 2 3 0 0 1
3 2
4 6 0
Is the red-blood-count in the two groups of patients the same?
Is the variation of red-blood-count in the two groups of patients the same?
3. There was examined the influence of temperature on the yield of technological process.
The results of experiment are shown in the table.
Temperature (◦C) Yield (g)
160 59, 61
160 50, 54
160 50, 58
180 56, 44
180 74, 70
180 81, 85
200 88.34
200 77.23
200 60.21
Analyze the experimental data and tell whether this factor has an influence on process yield or not. Comment on the obtained result.
4. Stack-losses of ammonia Y were measured in course of 21 days of operation of a plant for the oxidation of ammonia (NH3) to nitric acid (HNO3). The factors influencing stack losses were: the flow of cooling air x1 , the temperature of cooling water x2 , and acid concentration x3 . The experimental data is given in the table.
y 42 37 37 28 18 18 19 20 15 14 14 13 11 12 8 7 8 8 9 15 15
x180 80 75 62 62 62 62 62 58 58 58 58 58 58 50 50 50 50 50 56 70
x227 27 25 24 22 23 24 24 23 18 18 17 18 19 18 18 19 19 20 20 20
x389 88 90 87 87 87 93 93 87 80 89 88 82 93 89 86 72 79 80 82 91
Fit a multiple regression model to this data. Discuss the obtained results. Use the regression model to predict stack-loss of ammonia when x1=61 , x2=20 and
x3=85 .
