Consider the frequency distribution table (Table 14.3, Example 4, Chapter 14), which gives the weights of 38 students of a class. (i) Find the probability that the weight of a student in the class lies in the interval 46-50 kg. (ii) Give two events in this context, one having probability 0 and the other having probability 1.

Refer to Table 14.7 (i) Find the probability that a student obtained less than 20% in the mathematics test. (ii) Find the probability that a student obtained marks 60 or above.

Study the following Frequency distribution table and answer the question given below. Frequency Distrubution of Daily Income of 550 workers of a factory " " Table (i) What is the size of the class intervals? (ii) Which class has the highest frequency? (iii) Which class the lowest frequency? (iv) Which two classes have the same frequency?

Construct a frequency distribution table for the data on weights ( in kg.) of 20 students of a class using intervals 30-35,35-40 and so on. 40,38,33,48,60,53,31,46,34,36,49,41,55,49,65,42,44,47,38,39.

The height of 50 students, measured to the nearest centimetres have been found to be as follows: Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160-165, 165-170 etc.

An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table: Find the probabilities of the following events for a driver chosen at random from the city: being 18-29 years of age and having exactly 3 accidents in one year.

Two bodies of masses 1 kg and 3 kg respectively are connected rigidly by a vertical spring. The body of mass 3 kg rests on a smooth horizontal surface. The force constant of the spring is 484Nm^(-1) . From the equilibrium position, the mass of 1 kg is displaced vertically through a distance of 0.02 m and then released. calculate (i) and frequency of oscillation of the mass of 1 kg (ii) the maximum velocity of this mass (iii) its oscillation energy and (iv) the reaction of the table on the mass of 3 kg, when mass 1 kg is having harmonic oscillations.

An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table: Find the probabilities of the following events for a driver chosen at random from the city: being 30-50 years of age and having one or more accidents in a year.

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs. X and Rs y each and Rs Z each of the three respective values to 3,2 and 1 students respectively with a total award money of Rs 1600. School B wants to spend Rs 2300 to award its 4,1 and 3 students on respective values (b giving the same award money for the three values as before). If the total amount of award for one prize on each value is Rs 900 , using matrices find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.