A Company produces brake liners of thickness 6.4 mm. The company has four different machines to produce break liners. Each day five samples of each machine are taken and thickness of the break liner is determined. The following tables lists these details:

Perform an ANOVA using any software to test (at 5% level) whether all the four machines are producing the break lines with correct thickness. Justify your findings. Make suitable assumptions, if any.

A company manufactures milk packets of 1 litre. A sample of 20 such packet were taken out of a lot consisting of 1000 packets. The mean sample volume was found to be 1.0025 litre having a standard deviation of 0.04 litre. Assuming random sampling and a confidence level of 95%, will you accept the milk packets. Justify your answer. Make suitable assumption, if any.

Perform the following tasks using a spreadsheet (you may use spreadsheet function for computing the value of t):

(i) Find the value of t for the given value of degree of freedom and significance level (alpha):

Weight of students of a class having 40 student was recorded. This data is given in the following table. Perform the tasks given in (i) to (iv) on the data given below using a spreadsheet package:

(i) Find the minimum and maximum weight using the spreadsheet formula.

(ii) Create 6 classes with suitable class intervals and create the frequency distribution. You must use Array formula.

(iii) Find the percentage of the students whose weight is less than the mean weight

(iv) Draw the histogram for the data above. Also try to relate it to normal distribution curve.

List few applications of graph traversal schemes. For the following graph , write its adjacency list and adjacency matrix

Calculate storage requirement and time required to find edges in both the cases

Formulate a Knapsack problem and apply it to find an optimal solution for the following Knapsack problem. Use any two approaches:

• Kapacity of Knapsack: 25
• Number of Objects: 7

Write a general form of Greedy Technique.

Write and apply the partition procedure of Quick Sort algorithm to the following array. Show all the intermediate steps.

Answer the following questions related to run time behavior of this problem?

• How many times the loop will run?
• How many times the statements within the loop will run in each iteration?

Write Prim’s algorithm to calculate the minimum cost spanning tree of the following graph and calculate the time complexity of the algorithm. Show all the intermediate steps.

Discuss the limitations and strengths of Kruskal’s and Prim’s algorithm

What is the idea behind binary exponent evaluation? Write pseudocode to compute an using right to left and left to right binary exponentiation algorithm and perform its complexity analysis. Apply the algorithm to compute a55 and calculate the total number of multiplication operations in this case. How many multiplication operations are required if brute force multiplication method is used in this example? Show all the intermediate steps.

Write a Linear Search algorithm to search for a number 14 in the following list of integer numbers. How many search operations will be required in this example. Show all the intermediate steps.

Which are the other algorithms which perform better than the linear search algorithm? Discuss the worst case and average case time complexity of the algorithm.

Solve the following recurrence relation using recurrence tree and iteration methods

T(n) = T(n-1) + n

Define the recurrence relation of the following function

f(n)

(a) Describe the followings problems in brief and define its recurrence relation:

(i) Binary Search Problem

(ii) Tower of Hanoi Problem

Compute worst and best cases of time complexities of algorithm.When the worst and best cases of Bubble Sort algorithm would occur? Explain

Write important features of Bubble Sort algorithm. How is it different from Selection Sort and Insertion Sort algorithms in terms of the sorting processes? Apply Bubble Sort algorithm to do sorting of the following array of integer numbers in ascending order.

Write the pseudocode and show all the intermediate processes of the running of the code/algorithm

For the function defined by f(n) = 6 See Answer →

Define time complexity of an algorithm and calculate how many times the assignment operation will execute in the following code fragment

for( i = 1, i <= n, i++)

for (j = 1, j <= m, j ++) {

x = x + 1;