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#### Statistics and Probability Model Question Paper

10th Standard EM

Reg.No. :
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Maths

Time : 02:00:00 Hrs
Total Marks : 50
6 x 1 = 6
1. Which of the following is not a measure of dispersion?

(a)

Range

(b)

Standard deviation

(c)

Arithmetic mean

(d)

Variance

2. If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

(a)

3.5

(b)

3

(c)

4.5

(d)

2.5

3. The probability of getting a job for a person is $\frac{x}{3}$. If the probability of not getting the job is $\frac{2}{3}$  then the value of x is

(a)

2

(b)

1

(c)

3

(d)

1.5

4. A purse contains 10 notes of Rs.2000, 15 notes of Rs.500, and 25 notes of Rs.200. One note is drawn at random. What is the probability that the note is either a Rs.500 note or Rs.200 note?

(a)

$\frac{1}{5}$

(b)

$\frac{3}{10}$

(c)

$\frac{2}{3}$

(d)

$\frac{4}{5}$

5. A girl Calculates the probability of her winning in a match is 0.08 what is the probability of her losing the game

(a)

91%

(b)

8%

(c)

92%

(d)

80%

6. The variance of 5 values is 16. If each value is doubled. them the standard deviation of new values is_______

(a)

4

(b)

8

(c)

32

(d)

16

7. 9 x 2 = 18
8. Find the range and coefficient of range of the following data: 25, 67, 48, 53, 18, 39, 44.

9. The amount of rainfall in a particular season for 6 days are given as 17.8 cm, 19.2 cm, 16.3 cm, 12.5 cm, 12.8 cm and 11.4 cm. Find its standard deviation.

10. The amount that the children have spent for purchasing some eatables in one day trip of a school are 5, 10, 15, 20, 25, 30, 35, 40. Using step deviation method, find the standard deviation of the amount they have spent.

11. Find the mean and variance of the first n natural numbers.

12. The marks scored by the students in a slip test are given below.

 x 4 6 8 10 12 f 7 3 5 9 5

Find the standard deviation of their marks.

13. The mean and standard deviation of 15 observations are found to be 10 and 5 respectively. On rechecking it was found that one of the observation with value 8 was incorrect. Calculate the correct mean and standard deviation if the correct observation value was 23?

14. Two dice are rolled. Find the probability that the sum of outcomes is (i) equal to 4 (ii) greater than 10 (iii) less than 13.

15. What is the probability that a leap year selected at random will contain 53 saturdays. (Hint: 366=52 x 7 + 2)

16. A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3, …12. What is the probability that it will point to (i) 7 (ii) a prime number (iii) a composite number?

17. 2 x 5 = 10
18. The following table gives the values of mean and variance of heights and weights of the 10th standard students of a school.

 Height Weight Mean 155 cm 46.50 kg2 Variance 72.25 cm2 28.09 kg2

Which is more varying than the other?

19. If A and B are two events such P(A)=$\frac{1}{4}$, P(B)=$\frac{1}{2}$ and P(A and B) = $\frac{1}{8}$, find (i) P(A or B) (ii) P(not A and not B)

20. 2 x 8 = 16
21. The rainfall recorded in various places of five districts in a week are given below..

 Rainfall (in mm) 45 50 55 60 65 70 Number of places 5 13 4 9 5 4

Find its standard deviation.

22. The time taken (in minutes) to complete a homework by 8 students in a day are given by 38, 40, 47, 44, 46, 43, 49, 53. Find the coefficient of variation.