CUSTOMER_CODE SMUDE
DIVISION_CODE
EVENT_CODE
SMUDE
SMUAPR15
ASSESSMENT_CODE QM0012_SMUAPR15
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID 38071
QUESTION_TEXT
Define Poisson distribution. Write its probability distribution function, state its parameter. State 5 assumptions for applying the
Poisson distribution.
Poisson process is obtained when the binominal experiment is conducted many number of times. Here, the number of trials would be a large number. It is also a discrete probability distribution. If the probability of success ‘p’ is small and the number of trials ‘n’ is large, the binominal probabilities are hard to calculate. In such cases, when ‘n’ is large and ‘p’ is small, the binominal distribution are approximated to Poisson distributions. (2 M)
The probability distribution of a Poisson random variable X is given by;
SCHEME OF
EVALUATION
Where,
‘x’ varies from ‘0’ to infinity e = 2.71828, the base of nature logarithm m = Mean number of successes in the given time interval (2 M)
The mean and variance of the distribution is ‘m’. Its standard deviation is and ‘m’ is called the parameter of the distribution
(1 M)
Assumptions for applying the Poisson distribution
1. The outcome of trail/experiment must be of dichotomous nature
2. The probability of success must remain the same for trails
3. The trails should be conducted under identical conditions
4. The trails should be statistically independent
5. The probability of success should be very small and ‘n’ should be large such the ‘np’ is a constant m [Generally, p < 0.1 and n > 10]
(5 M)
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID 38072

QUESTION_TEXT
Define F-statistic, state its assumptions. State the assumptions for study of ANOVA
The ‘F’ statistic is defined as F = where S
1
> S
2
. It is used to test differences between variance, that is, whether two populations can be considered to have same variance or not. The sample variances
‘S
1
’ and ‘S
2
’ are calculated as:
= and
SCHEME OF
EVALUATION
=
Where, n
1
is the size of the first sample n
2
is the size of the second sample and denotes the sample means of the random variable ‘x’ and
‘y’ respectively
It is also known as variance ration test. It has two degrees of freedom, one for numerator of the ratio and another for denominator.
Assumptions:
1. The samples are simple random samples
2. The samples are independent of each other
3. The parent populations from which they are drawn are normally distributed.
Assumptions for study of ANOVA:
1. Each of the samples is a random sample
2. Population from which the samples are selected are normally distributed
3. Each of the samples is independent of the other samples
4. Each of the populations has the same variation and identical means
5. The effect of various components are additive
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID 73799
QUESTION_TEXT Briefly explain the concept of “Hypothesis”.
SCHEME OF
EVALUATION
“Hypothesis” is a statement about a population parameter subject to verification. Let us illustrate with an example. Suppose a Manager of a Car Company says “if we drop the price of this car model by Rs.
8000, we will sell 50,000 cars this year”, then such statement is

called a “hypothesis”. In simple words, we make a claim. Such claim is called a “Hypothesis”.
Let us see some of the examples of such statements or claims or
“Hypothesis”
1. The average speed of vehicles passing in the Mumbai City is
45 km/hr.
2. Eight percent of those who regularly play the state lotteries never win more than Rs. 100 in any one play
3. In 2009, the average starting salary in Marketing and Sales for a Post Graduate is
Rs. 20000 per month in metro cities of India.
4. The average number of kilometers driven by a Truck driver is
3800 km.
Hypothesis Testing
The terms “Testing a Hypothesis” and “Hypothesis Testing” are used interchangeably. Hypothesis testing begins with an assumption or statement, called a “hypothesis” that we make about a population parameter. In that statement, we assume a certain value for a population mean. We then develop a procedure to test the validity of such statement (hypothesis).
To test the validity of our assumption, we gather sample data and determine the difference between the hypothesized value and the actual value of the sample mean. Then we judge whether the difference is significance.
The smaller the difference, the greater the likelihood that our hypothesized value for the mean is correct. The larger the difference, the smaller the likelihood that our hypothesized value for the mean is correct. Unfortunately, the difference between the hypothesized population parameter and the actual statistic is more often neither so large that we automatically reject our hypothesis nor so small that we just as quickly accept it. So in hypothesis testing, as in most significance real-life decisions, clear-cut solutions are the exception, not the rule.
Assumptions
Although hypothesis testing sounds like some formal statistical term completely unrelated to business decision making, in fact managers propose and test hypothesis all the time.
Managerial hypothesis are based on intuition; the marketplace decides whether the manager’s intuitions were correct. Hypothesis testing is about making inferences about a population from only a small sample. The bottom line in hypothesis testing is when we ask ourselves (and then decide) whether a population, like we think this one, would be likely to produce a sample like the one we are looking at.
QUESTION_TYPE DESCRIPTIVE_QUESTION

QUESTION_ID 73801
QUESTION_TEXT Explain “Scatter Diagram”.
SCHEME OF
EVALUATION
A scatter diagram is a tool for analyzing relationships between two variables. One variable is plotted on the horizontal axis and the other is plotted on the vertical axis. The pattern of their intersecting points can graphically show relationship patterns. Most often a scatter diagram is used to prove or disprove cause-and-effect relationships.
While the diagram shows relationships, it does not by itself prove that one variable causes the other. In addition to showing possible cause and effect relationships, a scatter diagram can show that two variables are from a common cause that is unknown or that one variable can be used as a surrogate for the other.
A scatter plot can suggest various kinds of correlations between variables with a certain . Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the pattern of dots slopes from lower left to upper right, it suggests a positive between the variables being studied. If the pattern of dots slopes from upper left to lower right, it suggests a negative correlation. (10 marks)
QUESTION_TYPE
QUESTION_ID
QUESTION_TEXT
DESCRIPTIVE_QUESTION
120486
Write any 10 Characteristics of normal distribution.
Ten Characteristics of normal distribution (10 Marks)
1. Normal distribution is a continuous probability distribution
2. The equation for Normal distribution is given by:
SCHEME OF
EVALUATION
where, ‘x’ varies from -

to +

3. Its mean is μ and standard deviation is

where μ and

are the parameters of the distribution
4. It is a bell-shaped curve and is symmetric about its mean
5. The mean divides the curve into two equal portions
6. Its Quartile Deviation, Q.D = 2/3

.
7. Its Mean Deviation, M.D 4/5


8. The X – axis is an asymptote to the curve
[Asymptote is a straight line that touches the curve at infinity]
9. The point of inflexion occurs at

10. It is a unimodal distribution
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID
QUESTION_TEXT
120487
Write the Two primary reasons for which the process capability study is performed. Write 4 significance of it.
SCHEME OF
EVALUATION
A process capability study is performed for two primary reasons:
1. To predict future capability of the process to produce product within specification
2. To identify process improvement opportunities
(1 Mark each)
Four Significance of process capability
1. Process capability measurements allow us to summarize process capability in terms of meaningful percentages and metrics.
2. To predict the extent to which the process will be able to hold tolerance or customer requirements. Based on the law of probability, you can compute how often the process will meet the specification or the expectation of your customer.
3. You may learn that bringing your process under statistical control requires fundamental changes – even redesigning and implementing a new process that eliminates the sources of variability now at work.
4. It helps you choose from among competing processes, the most appropriate one for meeting customers' expectation.
(2 Marks each)