ASSIGNMENT SUBMISSION SHEET

Candidate Name

Student ID Number

Unit code

Centre NameUniversity of Wales Trinity Saint David

Course Title Data Handling & Statistics

Word Count (excluding bibliography)

Submission Date

Table of contents:

Name of the content Page No

Introduction3

Answer 13

Answer 25

Answer 36

Answer 47

Answer 58

Answer 69

Conclusion10

Reference and Bibliography10

Introduction:

Statistics is one of the time demanding courses for the present business world. At the second semester major and important statistical methods of analysis and equations has been taught by the course instructor which actually helped to prepare this assignment. This assignment has reflected with all the necessary and important statistical formula to answer the questions effectively. Basically to give appropriate solution to the problems and explain certain issues this assignment used the major key probability terms, probability distributions, sampling distributions, different proportions and parameters and the application of hypothesis.Answer to the question number: 11) Explaining the following terms with illustration:a) Dependent Variable: There are many types of variables among them independent and dependent variable are the essential for experimental and also for scientific study. Generally the dependent variable denotes those variable whose meaning is dependent on others, the value of the variable changes in the value of the others. In a causal relationship the dependent variables are the result of the causal variables which means in the experimental study the variables which is changed or affected with the degree of change into the other external variables that is actually dependent variable. Suppose that poverty has a direct relationship with the crime rate in society. In this case if we try to find out the cause and effect then the dependent variable would be the crime rate of the society which is an effect (Das, 2008). That is why it is called as responsible or measured variable.

b) Independent variables: In a causal statement we would find out two important factors among them one is because which is independent and have its own control and the other one is dependent or the effect which is controlled by the independent. Therefore an independent variable is such a variable which is free from any kind of influence and does not changed for other variables or any cause and obviously has its control over its value. The researcher can select such type of variables from the subject and can manipulate to change the behaviour of the dependent variable. Suppose if a doctor want to examine the mental stress of a patient with heart disease and found that stress is the cause for heart failure and other related disease. In this case the mental pressure would be the independent variable (Curwin, 2007).c) Discrete variable: Discrete variable generally indicates the individual state of variable where the numbers are never presented with fraction. A discrete variable could be defined as it is well defined finite set of possible values. Thus it cannot take all value which falls under the same limit or range. As for example if a boy is asked in his class room to count the total number of student at the class room, the student would have answer 20 or 40 but he can say 20.5 or 25.9. As the number of human cannot be fraction number. Whereas, the height of a person can vary for his height which could be 1 feet to 4.5 feet. This is continuous variable which can take on all other value with the limit. (Ahmed, 2006).d) Outliers: Outliers is such kind of data for which the point has to remain the main track of the total data set. In another definition, it is an observation which lies outside of the total number of distribution of data set. The outliers are very much common in the scatter diagram or even in the linear regression model. If the data fails to show any relationship thus proves his failure to the model. In the regression line for example if two individual data has been found far of the central linear diagram. Then these two will be used as outliers. (Moore and McCabe, 1999).e) Mutually exclusive events: It is such a situation where two or more events do not at same time and thus remain different with the result is called mutually exclusive events. According to Investopedia.com (2014) mutually exclusive events is such a situation where the occurrence of the one event is not influenced or caused by another event. For example, a dice of 6 different side with numbers if drawn then only one side would be shown, that is why two numbers at a time can not be seen as they are totally separated event.Answer to the question number: 2Tree Diagram of Playing Card can be shown as follows:

Source: Google Image (2013)

a) The probability of producing that all three draws high cards;

Suppose we assume that,

The total number of card, N= 52,

Low cards are, L= (Ace, 2, 3,4,5,6, and 7)

High card are, H= (8 , 9 ,10, Jack, king and Queen)

The total number of low cards in a set are, L=7x4=28 and

The total number of High cards in a set are, H=6x4=24.So, the probability of obtaining low card is, P(L)= 28/52 = 7/13

And probability of obtaining high card is, P(H)= 24/52 = 6/13

Now, in case of three set of cards it would be,P (HHH) = () = 216/2197 = 0.983 (Answer)b) The probability of getting low cards in all three different draws:From a total number of 52 cards the probability of getting the defined low cards would be 7/13. So, in case of three sets it would be,

P (LLL) = (7/137/137/13) = 343/2197= 0.1561 (Answer)c) The probability of producing more high cards than low cards:Discrete probability distribution formula would be appropriate in determining the probability of getting more high cards over the low cards. In case of producing the more high cards than the low cards is:P (LHH) + P (HLH) + P (HHL) + P (HHH)

= (7/13 6/13 6/13) + (6/13 7/12 6/13) + (6/13 6/137/13) + (6/13 6/136/13)=252/2157+252/2197+252/2197+216/2197

=0.1147+0.1147+0.1147+0.0983

=0.4424

Therefore the chance of getting more numbers of high cards over the low cards would be 0.4424. (Answer)Answer to the question number: 3a) Binomial distribution and its features:Binominal distribution is such a distribution which provides the probability of getting a specified number of successes for a defined number of independent trials and in the trials the probability of success would be same. The special feature of this distribution if in each trial the success would be same and the probability of getting success in each trial would be mutually exclusive. The conditions for binomial distribution would be the following: Each trail will have only two outcomes. The numbers of trials must be specified. The probability of getting success would be an mutually exclusive event where the data would be free. The probability of getting success in each trail will be same.The binomial distribution can be calculated using the following formula:

Where as q = 1-pb) An example of a binomial situation: To understand the binomial situation the appropriate example would be the case of Coin Tossing. In coin tossing case there are only to event which is completely different, one is head and the other one is tail, that is why there is two value. The probability of getting head will not cause any effect on the probability of getting tail as they are different and the chances would be same for both of the cases, that would be 50-50.

Answer to the question number: 44) From the formula of binomial distribution it can be deducted that the probability of getting x number of successes for n of trial:nCx px Qn-x = The symbol stands for,

N = the number of repeated trials

p = P(S) the probability of getting success in an individual trial

q = P(F) the probability of failure in an individual trial (q= 1-p)

x = The random variable represents a count of the number of successes in n trials: x = 0, 1, 2, 3, . . . n. Here,

n=15p=0.4q=(1-p)=(1-.4)=0.6So, lets find the followings:a) The probability that no sales are made:

From the formula we can say no sale made means, x = 0,So, P(X = 0) = 15C0 (.40)0 (.60)15-0= =110.00047

So, the probability of no sale made is 0.00047

b) The probability of making exactly 4 sales:Here, X=4So, P(X=4) = 15C4 (.40)4 (.60)15-4= =13650.02560.00363

=0.126

So, the probability of getting exactly 4 sales would be 0.126

c) The probability of fewer than 10 sales:Here, X=