**MS-8 Dec, 2009**

**MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS**

1.The following data describes the age at which employees reach to the level of 'senior manager in a multinational company

Age in years |
Below 34.5 |
34.5-37.5 |
37.5-40.5 |
40.5-43.5 |
Over 43.5 |

No of people reaching the leve |
14 |
60 |
95 |
24 |
7 |

**Find the quartile deviation.**

** **

2. In a bolt factory, machines A, B, C manufacture respectively 25%, 35% and 40% of the total production. Of their output 5%, 4% and 2% respectively are defective bolts. A bolt is drawn at random and is found to be defective. What is the probability that it is manufactured by machine B ?

3. Describe the design of stratified sampling. What is a strata ? Discuss about proportional allocation and disproportional allocation.

4. In a study to test whether there is difference between the average heights of adult females born in two different countries, random samples yielded the following results.

n1=120 , n2 = 150 , mean of x1=62.7 , mean of x2=61.8 and s1=2.50 and s2=2.62

where the measurements are in inches. Use 0.05 level of significance to test the difference between the average heights.

5. Find the most likely price of commodity A in Mumbai corresponding to the price of Rs. 70 at Kolkata from the following data.

Average Price in Kolkata Rs. 65

Average Price in Mumbai Rs. 67

Standard Deviation of prices in Kolkata Rs. 2.5

Standard Deviation of prices in Mumbai Rs. 3.5

Correlation coefficient between two + 0.8 prices in two towns

**6. Write short notes on any three of the following :**

a) Cramer's Rule.

b) Exponential Smoothing.

c) More than type ogive.

d) Cumulative Density Function (cdf) of a continuous random variable.

(e) Power curve of a test.

**7.In** a locality containing 18000 families a sample of 840 families was selected at random. Of these 840 families 206 families were found to have a weekly income of Rs. 500 or less. It is desired to know how many out of 18000 families have a weekly income of Rs. 500 or less. Use 3 sigma limits.

**8. A tour** operator charges Rs. 136 per passenger for 100 passengers with a discount of Rs. 4 for every group of 10 passengers in excess of 100. Determine the number of passengers that will maximize the amount of inoney the tour operator receives.