MATHEMATICS

Question # 5

Question # 5

The following results were obtained from interviews with the 500 people who changed their cars, recently, cars being classified as large, medium or small in size, depending on their length.

Present Large

Present Medium

Present Small

Total

Previous Large

75

47

22

144

Previous Medium

36

75

69

180

Previous Small

11

63

102

176

Total

122

185

193

500

(a) What proportion of people in the survey changed to:

(i) A smaller car;

Present small car

193

Total survey

500

Changed to small Car

0.386

Not Changed to Small car

0.614

(ii) A larger car;

Present Large car

122

Total survey

500

Changed to Large Car

0.244

Not Changed to Large car

0.756

(b) What effect would such car changing habits have generally on the size of the car owned in the future?

After the above results, it can be said that the car changing habits of the people have generally depends on the size of the car owned by the individuals. Moreover, it can be said that the most of the people who are changing their cars are moving towards the small cars and not to the large or the medium cars. This habit could happen or taking place due to various reasons like size, price etc. In addition to this, it is observed that most of the people are satisfied with their existing or the previous cars as they do not prefer to change their previous or the existing cars.

(c)

(i) What is the probability that a person from the survey selected at random who bought a large car previously had a small or medium car?

Bought large car

75

Previous car

500

Probability of a person who bought a large car

0.15

The probability of a person randomly selected, who bought a large car has 0.15 probabilities that he will buy a large car. Therefore, there is not too much probability that this situation may happen. The probability distribution is rigorously called the standard normal distribution in probability and statistics textbooks and in the literature. A random variable with a standard normal distribution is called a standard normal random variable. Because probability is usually used to represent a standard normal random variable, the standard normal distribution is sometimes called the probability distribution for convenience by practitioners. In the following, the convention of representing a random variable with a capital letter and a specific value of the random variable with the corresponding lowercase letter is used (Evans, 2000).

The standard normal distribution is one of the most important probability distributions in probability theory and statistics. Many random phenomena follow a normal distribution or approximately a normal distribution and can be represented by a normal random variable. A normal random variable can be transformed into a standard normal random variable through standardization. Many other random variables, such as the ?2 random variables, the t random variables, and the F random variables, can be written as functions of the standard normal random variable. The laws of probability are a collection of equations that define probabilistic relationships among events (Everitt, 1999).

The validity of each equation, or probability law, often depends on the events having met certain conditions. Thus, each law is accompanied by a list of what, if anything must be assumed about the events in question for the ...