Business Statistics and Operations Management Questions and Answers

Answer: A

Batch production suits medicine production, where products such as tablets and syrups are made in lots, with a definite quantity processed together and a batch number for traceability. Sugar and petroleum products are made by continuous process industries with uninterrupted flow of material. Agriculture produce is grown, not produced in batches on a plant. In batch production a limited number of units of a product is made in one run, after which the equipment is cleaned or reset for another product or lot, which suits drugs where each lot has to be tested and traced. So A is correct.

Answer: D

Residential Layout is not a type of plant layout.

The standard types are the product (line) layout, where machines are arranged in the order of operations for one product; the process (functional) layout, where similar machines are grouped together; the fixed position layout, where the product stays in one place and men and machines come to it, as in shipbuilding; and the combination layout. Product Layout (A), Process Layout (B) and Fixed Position Layout (C) are all in that list. A residential layout is a term from housing and town planning and has no place in the arrangement of production facilities.

Answer: D

All three factors are considered, so the answer is All the above.

Plant location decisions weigh the nearness of raw material sources, which cuts transport cost for weight-losing materials (A), the availability of water, which matters for process industries, power plants and cooling (B), and marketing facilities, meaning closeness to customers and distribution channels (C). Labour, power, transport, climate and government incentives are others. Since (A), (B) and (C) are each genuine location factors, choosing only one of them leaves out the other two.

Answer: A

Work measurement refers to the length of time it takes to complete a work task assigned to a specific job.

It is the application of techniques, such as time study and work sampling, to establish the time a qualified worker needs to carry out a specified job at a defined level of performance, and so to set time standards. Improving work methods (B) is method study, its companion technique. Arrangement of machines according to sequence of operations (C) describes a product layout. Planning the work and working the plans (D) is a general statement about the management function of planning, and says nothing of measuring time.

Answer: B

The graphical method can be used to solve a linear programming problem with two decision variables.

The method plots the constraints on a two-axis graph, finds the feasible region and checks its corner points, so it is limited to two variables (axes). It is not limited to integer data (A), and it cannot handle any linear programming problem (C), because three variables need a three-dimensional picture and larger problems need the simplex method. A transportation problem with two origins and two destinations (D) has four variables (the shipping quantities), so it is not a two-variable graph, and it is usually solved by transportation algorithms.

Answer: B

The probability is 1/12.

Two dice give 36 equally likely outcomes. A sum greater than 10 means a sum of 11 or 12. \(11\) comes from (5,6) and (6,5), and \(12\) comes only from (6,6), so there are 3 favourable outcomes.

\[ P = \frac{3}{36} = \frac{1}{12} \]

1/9 would be 4/36, which counts one outcome too many, 1/18 is 2/36 and counts only (5,6) and (6,5), and 1/3 is far too large for sums this rare.

Answer: A

The mean is 8 and the variance is 4, so the answer is 8, 4.

For a binomial distribution with sample size \(n\) and probability of success \(p\):

\[ \text{mean} = np = 16 \times 0.5 = 8 \]

\[ \text{variance} = npq = 16 \times 0.5 \times 0.5 = 4 \]

Option (B), 8 and 8, would be right for a Poisson distribution, where mean and variance are equal. Options (C) and (D) give a mean of 4, which is what you get by taking \(npq\) as the mean. For a binomial the variance is always less than the mean.

Answer: B

Two variables are perfectly negatively correlated if the coefficient of correlation between them is -1.

The correlation coefficient lies between -1 and +1. A value of +1 means perfect positive correlation, 0 means none, and -1 means perfect negative correlation, with all points on a straight line sloping down. A positive covariance (A) signals positive correlation, and a negative covariance (C) only shows that the correlation is negative, not that it is perfect, because covariance has no fixed limits and depends on units. 'None of the above' (D) is wrong because (B) is the exact definition.

Answer: C

The appropriate method is Stratified Sampling.

When a population falls into well-defined groups that are homogeneous within and heterogeneous between, the sample is drawn from every group (stratum), usually in proportion to its size. This gives better precision than simple random sampling. Cluster sampling (A) is used when the groups are internally varied but alike one another, so any few clusters represent the whole, which is the reverse of this description. Simple random sampling (B) ignores the group structure, and judgement sampling (D) rests on the researcher's choice rather than a probability design.

Answer: B

The correct matching is I-4, II-2, III-3, IV-1, which is code 4 2 3 1.

For a Poisson distribution the mean and variance are equal (I-4). The normal distribution is symmetric about its mean (II-2). The chi-square distribution is positively skewed, with a long right tail (III-3). The binomial distribution has mean \(np\) greater than variance \(npq\), because \(q\) is less than 1 (IV-1). Option (A) gives chi-square a mean greater than variance, and options (C) and (D) put the symmetric normal distribution against the wrong property, so they fail at the second or third pair.