EIT Mathematics and Statistics 3

Question 1

What is the solution to the first-order ODE dy/dx = 2y with y(0) = 3?

Accepted Answer

y = 3e^(2x)

Answer

Separating variables and integrating gives y = Ce^(2x); applying y(0)=3 yields C=3, so y = 3e^(2x).

Question 2

A normal distribution has mean 50 and standard deviation 10. What percentage of data falls within one standard deviation?

Accepted Answer

68%

Answer

The empirical rule states approximately 68% of data falls within ±1 standard deviation of the mean.

Question 3

Which method is used to solve a system of linear equations by converting the augmented matrix to row echelon form?

Accepted Answer

Gaussian Elimination

Answer

Gaussian Elimination uses row operations to transform the augmented matrix into upper triangular form, enabling back substitution.

Question 4

The inverse Laplace transform of 1/s² is:

Accepted Answer

t

Answer

The inverse Laplace transform of 1/s² is t, since L{t} = 1/s².

Question 5

What is the probability that a standard normal variable Z is less than 1.96?

Accepted Answer

0.975

Answer

From standard normal tables, P(Z < 1.96) ≈ 0.975, leaving 2.5% in the upper tail.

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