Math Answers

Question One

The manufacturer of a new car claims for it an average mileage of 60 km per litre with a standard deviation of 2 km under city conditions. However, the mileage in 64 trials is found to be 57 km.

Test to determine if the manufacturer’s claim is justified at 5% level of significance.                                                                                                                                                (6 marks)

i)                                  Construct the 99% confidence interval estimate for the mean mileage            (2 marks)

Which of the following pairs of statements are logically equivalent?

   I.   Statement 1: It is not true that both you have pneumonia and I got flu.

       Statement 2: Either you have no pneumonia or I have no flu.

   II.   Statement 1: It is not true that either I watched 'Crashlanding on You' or you watched 'Money Heist'.

       Statement 2: I did not watch 'Crashlanding on You' and you watched 'Money Heist'.

a) II only

b) I only

c) I and II

d) Neither I nor II

Consider that an object weighing 50 lb is dropped from a height of 1000ft with zero initial velocity. Assume that the air resistance is proportional to the velocity of the body. If the limiting velocity is known to be 200ft/sec, find the time it would take for an object to reach the ground.

a. How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of four aces (A) are chosen?

the upper triangular n x n matrices with no zeros on the diagonal

5x +2y +z =-8

x -2y -3z =0

-x +y +2z =3

Solved this problem by using Gauess Gordan method.

1. Discuss ways in which the current telephone numbering plan can be extended to accommodate the rapid demand for more telephone numbers. (See if you can find some of the proposals coming from the telecommunications industry.) For each new numbering plan you discuss, show how to find the number of different telephone numbers it supports.
2. Describe at least one way to generate all the partitions of a positive integer n. (You can get idea from Exercise 49 in Section 5.3.)
3. Proof that an undirected graph has an even number of vertices of odd degree.
4. In Exercises i) and ii) determine whether the given graph has a Hamilton circuit. If it does, find such a circuit. If it does not, give an argument to show why no such circuit exists.

The weight of the 5 grade boys is assumed to have normally distributed with mu = 0 kg and sigma = 5 kg find:

The area under the normal curve to the left of point 34kg. What does this area indicate?

The population of fish in a particular pond is known to have a mean length µ = 15 cm with standard deviation σ = 5. You catch fifty fish from the pond and measure their lengths. What is the probability that the average length of those fish (i.e. sample mean X ) is between 14 cm and 16.5 cm?

The population of fish in a particular pond is known to have a mean length µ = 15 cm with standard deviation σ = 5. You catch fifty fish from the pond and measure their lengths. What is the probability that the average length of those fish (i.e. sample mean X ) is between 14 cm and 16.5 cm?