Assignment – I

Q.1 Two hundred persons were interviewed by a public opinion polling agency. The frequency distribution gives the ages of persons interviewed.Find the average.

Age groups (yr.) Frequency( f) Age groups (yr.) Frequency( f)80 – 89 2 40 - 49 5670 – 79 2 30 - 39 4060 – 69 6 20 - 29 4250 – 59 20 10 - 19 32

Q.2 Find the average marks of students from following data :

Marks Above 0

Above 10

Above 20

Above 30

Above 40

Above 50

Above 60

Above 70

Above 80

Above 90

Above 100

No. of students

80 77 72 65 55 43 28 16 10 8 0

Q.3 An incomplete frequency distribution is given as follow:

Variable 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Totalfrequency 12 30 ? 65 ? 25 18 229

Given that the median value is 46, determine the missing frequencies.

Q.4 Find the quartile range of the given data:

Class 0 - 6 6 - 12 12 – 18 18 – 24 24 - 30Frequency 8 10 12 9 5

Q.5 Age distribution of hundred life insurance policy holders is as follows:

Ages as on nearest birthday

17-19.5 20-25.5 26-35.5 36-40.5 41-50.5 51-55.5 56-60.5 61-70.5

Number 9 16 12 26 14 12 6 5Calculate variance and standard deviation.

Q.6 Mr. X has 2 shares in a lottery in which there are 2 prizes and 5 blanks. Mr. Y has 1 share in a lottery in which there is 1 prize and 2 blanks. Show that the chance of Mr. X’s success to that of Mr. Y’s as 15:7.

Q.7 The probability that a trainee will remain with a company is 0.6 . The probability That an employee earns more than Rs 10,000 per month is 0.5. The probability That a employee whonis a trainee remained with the company or who earns more Than Rs 10,000 per month is 0.7. What is the probability that an employee earns more than Rs 10,000 per month gives that he is trainee who stayed with the company?

Q.8 There are three similar coins one of which is ideal and other two are biased. The chances of head are respectively 1/3 and 2/3. A coin is selected at random and tossed twice. If head occurs both times, find the probability that the ideal coin was selected.

Q.9 A speaks the truth 3 times out of 4 and B 5 times out of 6, they agree in stating a white ball has been drawn from a bag which was known to contain 2 white and 8 black balls. Find the chance that the white ball is really drawn.

Q.10 “A” speaks truth 2 times out of 3 and “B” 4 times out of 5; they agree in the assertion that from a bag containing 6 balls of different colours a red ball has been drawn, Find the probability that the statement is true.

Q.11 The probability that the principal of a college is in good mood is 0.6 and the probability that he agrees to suggestions of a professor, when in good mood, is 0.4 If he is not in a good mood, the probability of agreeing to suggestions is 0.1 On a certain day when he (Principal) agrees to the suggestions of a professor, what is the probability that he was in good mood?

Q.12 A and B are two very weak students of Statistics and their chance of solving a problem correctly are 1/8 and 1/12 respectively. If the probability of their making a common solution is 1/1001 and they obtain same answer, find the chance that their answe is correct.

Q13. A box contains 3 blue and 2 red balls while another box contains 2 blue and 5 red balls. A ball is drawn at random from one of the boxes turns to be blue. What is the probability that it came from the first box?