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problem 1) Total scores X obtained by 50 students in Statistical Technique test of 100 marks are given below:

80    90    85    55    40    50    40    95    81    82
75    70    80    40    10    55    30    80    80    72
27    95    20    30    85    10    40    23    75    60
50    30    10    10    90    15    20    40    70    65
45    50    40    10    90    20    25    42    70    70

(i) prepare the formula for finding minimum and maximum scores.

(ii) Draw the frequency distribution using descriptive statistics.

(iii) Compute the percentage of students, who scored above the pass marks of 50.

(iv) Compute the number of students, who scored between 50 and 80?

problem 2) Canned juice company needs to find out mean weight of the can of canned juice. It takes a random sample of 80 such cans (from some thousand cans in its warehouse) and finds that mean weight is 201.15 grams and the standard deviation is 0.56 grams. Detemine a 95% confidence interval for the mean weight of the cans in the firm warehouse.

problem 3) A chemical firm wishes to find out how four catalysts differ in yield. Firm runs the experiment in eight of its plants type. In each plant, yield is measured with each catalyst. yield (in Quintals) is as follows:

Plant          Catalyst
             1    2    3    4
A           2    1    2    4
B           3    2    1    3
C           1    3    3    1
D           5    4    3    2
E           1    2    4    3
F           2    1    1    2
G          4    3    4    2
H          3    1    4    3

Carry out an ANOVA using any software and comment whether yield due to the particular catalyst is significant or not at 5% level of significance. Make appropriate assumptions, if any.

problem 4) Sales figure of the textile company is given below. Utilize software to determine the moving averages for the length of 5.

Day    Sales
1         230
2         200
3         250
4         300
5         200
6         225
7         400
8         450
9         415
10       420
11       500
12       300
13       400
14       300
15       315

problem 5) A company manufactures pipes of small diameter. Five observations of diameters of the pipe produced were taken periodically. Following table gives average of these 5 observations, taken 12 times during the working day. Compute the control limits for mean and range, and plot the control charts using any statistical software.

The data is given below in the following table:

Sample No.            Sample values                           Sample mean

1                        4.06, 4.08, 4.08, 4.08, 4.10               4.08
2                        4.10, 4.10, 4.12, 4.12, 4.12               4.112
3                        4.06, 4.06, 4.08, 4.10, 4.12               4.084
4                       4.06, 4.08, 4.08, 4.10, 4.12                4.088
5                       4.08, 4.10, 4.12, 4.12, 4.12                4.108
6                       4.08, 4.10, 4.10, 4.10, 4.12                4.100
7                      4.06, 4.08, 4.08, 4.10, 4.12                 4.088
8                      4.08, 4.08, 4.10, 4.10, 4.12                 4.096
9                      4.06, 4.08, 4.10, 4.12, 4.14                 4.100
10                    4.06, 4.08, 4.10, 4.12, 4.16                 4.104
11                    4.12, 4.14, 4.14, 4.14, 4.16                 4.140
12                    4.14, 4.14, 4.16, 4.16, 4.16                 4.152
 (d2 = 2.326, d3 = 0,  d4 = 2.11, A2 = 0.58)

problem 6) Fit the linear trend using any statistical software to data collected in the unit manufacturing umbrellas, given in following table.

Month        1      2      3      4      5      6
Demand    46    56    54    43    57    56

Statistics and Probability, Statistics

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