MatLAB Answers

11. The battery life of a certain battery is normally distributed with a mean of 90 days and a standard deviation of 3 days.

For each of the following questions, construct a normal distribution curve and provide the answer.

a)    About what percent of the products last between 87 and 93 days?

b)    About what percent of the products last 84 or less days?

For each of the following questions, use the standard normal table and provide the answer.

c) About what percent of the products last between 89 and 94 days?

d) About what percent of the products last 95 or more days? 

• Do the calculations on Matlab, print it out and then write your answers on the attached answer

sheet.

• Attach your Matlab printout to your answer sheet before you hand in.

1. Find all solutions for each of the following systems of equations (if the system is consistent):

(a) 6.5x − 2y = 7 (b) 3.5x1 + 4.5x2 + 5.5x3 = 11

2x − 0.75y = 1.75 x1 + 4x2 − 7x3 = −16

12x − y = 21 0.5x1 − 0.75x2 + 0.75x3 = 3.5

(c) − 0.75x1 + 0.75x2 = −6

2.5x1 + 2x2 − 4.5x3 = 2

1.25x1 + 1.25x2 − 2.5x3 = 0

(d) 3.4x1 + 3.4x2 − 15.3x3 = −20.4

0.5x1 + 0.25x2 − 0.75x3 = 1

0.75x1 + 0.5x2 − 1.5x3 = 1

Please note: You should use Matlab to write your systems in reduced row echelon form, but have to

interpret the results and give the solution(s) if the system is consistent.

The “Titans” cricket team has a winning rate of 75%. The team is planning to play 10 matches in the next season.

a)    Let X be the number of matches that will be won by the team. What are the possible values of X?

b)    What is the probability that the team will win exactly 6 matches?

c)    What is the probability that the team will lose 2 or less matches?

d)    What is the mean number of matches that the team will win?

e)    What are the variance and the standard deviation of the number of matches that the team will win?

write the Mathlab statement requried to calculate y(t) from the equation of y(t)={-3t² + 5, t>=0

3t² +5,t<0

write the mathlab statement required to calculate y(t) from the equation y(t)= -3t²+5

1.    Two fair cubes are rolled. The random variable X represents the difference between the values of the two cubes.

a)    Find the mean of this probability distribution. (i.e. Find E[X])

• Do the calculations on Matlab, print it out and then write your answers on the attached answer

sheet.

• Attach your Matlab printout to your answer sheet before you hand in.

1. Find all solutions for each of the following systems of equations (if the system is consistent):

(a) 6.5x − 2y = 7 (b) 3.5x1 + 4.5x2 + 5.5x3 = 11

2x − 0.75y = 1.75 x1 + 4x2 − 7x3 = −16

12x − y = 21 0.5x1 − 0.75x2 + 0.75x3 = 3.5

(c) − 0.75x1 + 0.75x2 = −6 (d) 3.4x1 + 3.4x2 − 15.3x3 = −20.4

2.5x1 + 2x2 − 4.5x3 = 2 0.5x1 + 0.25x2 − 0.75x3 = 1

1.25x1 + 1.25x2 − 2.5x3 = 0 0.75x1 + 0.5x2 − 1.5x3 = 1

Please note: You should use Matlab to write your systems in reduced row echelon form, but have to

interpret the results and give the solution(s) if the system is consistent.

The Gaussian distribution also known as the Normal distribution, is given by the following

equation:

𝑦(𝑥) = 𝑒𝑥𝑝 −(𝑥−𝜇)^2/2𝜎^2

where parameter 𝝁 is the mean and 𝝈 the standard deviation.

(i) Write a MATLAB code to create a 1000 point Gaussian distribution of random numbers

having 𝜇 = 0 and 𝜎 = 1. (20)

(ii) Plot this distribution. (10)

(iii) Prove that the full width–half maximum (FWHM), of the above distribution is given by :

FWHM = 2𝜎√2ln 2 (10)

The Gaussian distribution also known as the Normal distribution, is given by the following

equation:

𝑦(𝑥) = 𝑒𝑥𝑝 −(𝑥−𝜇)^2/2𝜎^2

where parameter 𝝁 is the mean and 𝝈 the standard deviation.

(i) Write a MATLAB code to create a 1000 point Gaussian distribution of random numbers

having 𝜇 = 0 and 𝜎 = 1. (20)

(ii) Plot this distribution. (10)

The Gaussian distribution also known as the Normal distribution, is given by the following

equation:

𝑦(𝑥) = 𝑒𝑥𝑝 −(𝑥−𝜇)^2/2𝜎^2

where parameter 𝝁 is the mean and 𝝈 the standard deviation.

(i) Write a MATLAB code to create a 1000 point Gaussian distribution of random numbers

having 𝜇 = 0 and 𝜎 = 1. (20)

(ii) Plot this distribution. (10)