Quantitative Methods Answers

Find an interval of unit length which contains the smallest negative root in magnitude
of the equation 12 0
3
x + x + = . Taking the midpoint of this interval as initial
approximation and using Newton-Raphson method find the root correct to three
decimal places.

If 7000 dollars is invested in a bank account at an interest rate of 7 percent per year, compounded continuously. How many years will it take for your balance to reach 10000 dollars?

a sample fo 6 skyline student was selected and data about their anxiety in taking exams and tests for the spring exam 2014 and the data was recorded as shown in the table..
anxiety score test score after exam (%)
10 2
8 3
2 9
1 7
5 6
6 5

Using Regula Falsi method approximates the root of the following equation upto four decimal places.

f(x)=x=e power -x

A SAMPLE OF 400 STUDENTS OF UNDERGRADUATE AND 400 STUDENTS OF POST
GRADUATE CLASSES WERW TAKEN TO KNOW THIR OPENION ABOUT AUTONOMUS
COLLEGE. 290 OF THE UNDERGRADUATE AND 310 OF THE POST GRADUATE
STUDENTS FAVOURED THE AUTONOMUS STATUS .PRESENT THESE FACT IN THE FORM
OF A TABLE AND TEST AT 5% LEVEL , THAT THE OPINION REGARDING AUTONOMUS
STATUS OF COLLEGES ARE INDEPENDENT OF THE LEVEL OF CLASSES OF STUDENTS

3. A sample of 400 students of undergraduate and 400 students of post graduate classes were taken to know their opinion about autonomous college. 290 of the undergraduate and 310 of the post graduate students favoured the autonomous status. Present these fact in the form of a table and test at 5% level, that the opinion regarding autonomous status of colleges are independent of the level of classes of students

Suppose you have a wire mesh which is N by M units long, made up of unit square with wire at the edges. (So there are N+1 parallel wires all M long and, perpendicular to these, M+1 all N long).An ant starts off at the bottom left corner of this grid (co-ordinates (0,0) and crawls on the wires the shortest possible distance to reach the top-right corner (N,M). How long is the shortest route. How many different shortest routes are there? (Namely, find a formula in terms of N and M) You might want to try this for small values of N and M and see if you can work out how the number for (N,M) relates to those for (N,M-1) and (N-1,M) If you build up a table of these numbers you might recognise them from elsewhere in mathematics so that might help you find the formula, but you also try to explain the connection.

Price of the ticket for movie THE LORD OF RINGS in a cinema is Rs.50. When the price of the ticket was lowered, the number of visitors increased by 60% and the box office collection increased by 36%. Find the reduction in the ticket price.
A man bought 1,000 shares each of face value Rs. 5 at Rs. 7 per share. At the end of the year, the company declared a dividend of 8%. Calculate

(a) the amount of money invested by the man.

(b) the percentage return on his outlay, correct to nearest paise.

The following two samples are of two classes of students taking the same course. One group of students takes the same course in the morning and the second group takes the class in the evening. The grade distributions are as follows:

ID Morning Group Evening Group

1 15 5
2 13 4
3 14 5
4 15 3
5 12 10
6 12 1
7 11 2
8 12 3
9 11 4
10 10 5

Carry a t-test to see any difference between the morning and evening groups. Use Excel to find the p-value and indicate whether the results are significantly different or not.

The bulbs manufactured by a company gave a mean life of 3000 hours with standard
deviation of 400 hours. If a bulb is selected at random, what is the probability it will
have a mean life less than 2000 hours?
Question:
1) Calculate the probability.
2) In what situation does one need probability theory?
3) Define the concept of sample space, sample points and events in context of
probability theory.
4) What is the difference between objective and subjective probability?