# NMIMS Solved Assignments

## Sep 2020 Business Stats

Q1. The sales figures of two firms (in million Rs.) calculated over a period of time are as follows:

Firm A | 120 | 100 | 110 | 80 | 90 | 70 | 50 | 60 | 40 |

Firm B | 50 | 40 | 60 | 90 | 80 | 70 | 110 | 100 | 120 |

- Find mean and standard deviation of both the firms and interpret the same.
- Which firm has better performance? How do you analyze the performance in this case?
- If you need to invest in a firm then which firm would you choose and why?

Q2. The Manager wants to fix income of employees for production department. The past data on 8 incomes with the experience is shown below

Experience (in years) | 10 | 12 | 6 | 7 | 10 | 8 | 1 | 5 |

Income (in thousands) | 25 | 28 | 17 | 18 | 24 | 21 | 10 | 16 |

- Find the correlation between the experience and income.
- Determine the coefficient of determination and interpret it.
- Estimate the monthly salary for a person having 14 years of experience by assuming the linear relation between the two variables.

Q3. The weekly demand of a cell phone shop is following the normal distribution with average number of cell phones sold is 200 units and it has also been found that 90% of time the demand is lying less than 220 units.

- Using this information find the standard deviation of the distribution.
- Determine the lowest stock that the company should maintain so that the probability of shortage is not higher than 5%.

### Previous June 2020

Q1. For the given data set representing the runs scored by two players in last 15 matches, conduct the following analysis:

i. Which average you will use to summarize the performance of the player? Find average runs scored for both of the players. Also give reasons for the choice of the average?

ii. If selection is possible on the basis of consistency, which player would you choose in the team? Perform the required statistics and justify the selection.

iii. Check whether there exists any relationship among the runs scored by two players using Karl Pearson coefficient of correlation and interpret the same.

Q2. On the basis of the following data, the marketing manager wants to predict the sales volume for the locality on the basis of # households, number of cars and marketing expense

i. Draw three scatter plots of sales volume with each of the three variables and comment on their correlation.

ii. Regress the sales volume on #household, number of cars and marketing expense. Calculate R square and interpret the same.

iii. Determine which variable is/are significant variable/s. Is there any insignificant variable? If yes, regress again, by dropping the variable. Will dropping that variable increases the adjusted R square?

Q3. a. The height of the students in a certain class is following normal distribution with mean height as 165 cm and standard deviation of 25 cm. There are 60 students in that class. Determine

- The number of students whose height is more than 158 cm.
- The number of students whose height is lying between 155 and 172 cm.

- b. Find the lowest height among the tallest 5 student in a class.

## Old Assignment Queustion

- A sample of 20 bulbs each was picked from the manufacturing facility of two bulb manufacturers – Mfr 1 and Mfr 2. The table above provides the life of bulbs for the two manufacturers. You are a quality testing person and are presented with this data:

i. Which manufacturer has better performance on the life of bulbs? What are the different measures you can consider to calculate performance?

ii. How would you assess the variability in performance of the two bulb manufacturers?

iii. Would your answer to the first question change based on your assessment of the variability in performance of bulb manufacturers? - For the data in the table below: (10 Marks)
- i. What do the correlation coefficients of 1, shaded in yellow, indicate?
- ii. The highest correlation coefficient is 0.84, shaded in green. What can you infer from that score about the relationship between the two variables?
- iii. The two lowest correlation coefficients are 0.06 and -0.06. What can you infer from that score about the relationship between the two variables?

- The Indian cricket team is visiting New Zealand to play a test series comprising five matches. In each match, assume that the Indian team has a 70% chance of winning. Further, assuming that the matches are independent of each other, what is the probability that:

a. The Indian team will win the series? (5 Marks)

b. The team will win all five matches, and that the team will lose all? (5 Marks)