25 samples of 6 items each were selected from the assembly line of a machine. On
measurement of a critical dimension, the mean X of 25 sample means was reported
as 0.81 inches and  as 0.0025 inches. Compute the control limits for the X and
R charts.

If the random variable X is normally distributed with mean 80 and standard deviation
5, then find (i) P[60.5 < X < 90], and (ii) P[X _ 80 < 1].

There are 1000 pages in a book out of which 100 pages are defective. What is the
probability that out of first 50 pages 10 pages will be defective?

Write three advantages and three limitations of systematic sampling

 In a locality, 100 persons were randomly selected and asked about how far they had studied. The results are shown in table given below

The frequency distribution of marks of 230 students in a statistics paper in a class is given below:
Class Interval              Frequency
10 – 20                            12
20 – 30                             30
30 – 40                               ?
40 – 50                             65
50 – 60                               ?
60 – 70                              25
70 – 80                             18
Total 230
Given that the median value of distribution is 46, determine the missing frequencies.

A hospital has 25 centres located at different places in a state. Each centre has been provided with 4 paramedics. In order to estimate the average number of patients handled by a paramedic on a typical day at a centre, a sample of 5 centres was selected, using without replacement simple random sampling. The data regarding the number of patients on a typical working day for each selected centre are given below: