1. The mean and standard deviation of 20 items is found to be 10 and respectively. At the time of checking it was found that one noted item with value 8 was incorrect. Calculate the mean and standard deviation, if the wrong item is deleted.

2. Let X1 and X2 be two independent random variables with variances Var(x1) Var(x2) =2. If the variance of y =3x2 -X1 is 25, then find k.

3.(a) State and prove the Addition theorem of probability.
Suppose that A and B are two independent events, associated with a random experiment. The probability of occurrence of event A or B is 0.8, while the probability of occurance of event A is 0.5. Determine the occurrence of probability of event B.

4.(a) What do you understand by a random variable Define the types of random variables.
A bag contains 10 white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. Find the probability that all black balls are drawn by the 6th draw.

5. A survey of 64 medical labs revealed that the mean price charged for a certain test was Rs 120, with a standard deviation of Rs 60. Test whether the data indicates that the mean price of this test is more than Rs 100 at level of significance.

6. Describe the following tests in detail Paired t-test Chi-Square test for independence of Attributes

7. Differentiate between any two of the following:
Simple Random Sampling With Replacement and Simple Random Sampling Without Replacement Probability (Random) Sampling and Non-Random Sampling One-Sample Test and Two-Sample Test

8. The following table shows the sample values of 3 independent normal random variables. Test whether they have the same mean [use ANOVA].Given F0.05 =4·26.
<img src='./qimages/10570-8.jpg'>

9.(a) Discuss the following: Control chart for variables

(ii) Control chart for attributes Describe control chart for X and R in detail. Also suggest when R-chart and S-chart can be used.