EIT - Engineer In Training Mathematics and Statistics Questions and Answers

Question 1

Two independent events, A and B, have probabilities P(A) = 0.3 and P(B) = 0.5. What is the probability that either event A or event B will occur, P(A ∪ B)?

Accepted Answer

0.65

Answer

0.80

Answer

0.15

Answer

0.50

Question 2

An engineering firm is analyzing the compressive strength of a new concrete mix. The following five test results (in MPa) were recorded: 30, 32, 35, 38, 40. What is the sample standard deviation of these measurements?

Accepted Answer

4.32 MPa

Answer

4.00 MPa

Answer

3.5 MPa

Answer

18.5 MPa

Question 3

What is the determinant of the following 3x3 matrix?
| 2  1  0 |
| 3 -1  4 |
| 5  2  0 |

Accepted Answer

-22

Answer

1

Answer

0

Answer

22

Question 4

Which of the following is the correct formula for integration by parts?

Accepted Answer

∫ u dv = uv - ∫ v du

Answer

∫ u dv = uv + ∫ v du

Answer

∫ u/v dx = (v u' - u v') / v^2

Answer

∫ u v dx = (∫ u dx) * (∫ v dx)

Question 5

A quality control engineer is inspecting a batch of 100 resistors. The mean resistance is 1000 ohms, and the mode is 990 ohms. The median resistance is 995 ohms. Which statement is most likely true about the distribution of resistance values?

Accepted Answer

The distribution is positively skewed (skewed to the right).

Answer

The distribution is symmetrical.

Answer

The distribution has no clear central tendency.

Answer

The distribution is negatively skewed (skewed to the left).

Question 6

What is the general solution to the first-order linear differential equation dy/dx + 2y = 6?

Accepted Answer

y = 3 + Ce^(-2x)

Answer

y = 3 + Ce^(2x)

Answer

y = Ce^(-2x)

Answer

y = 3e^(-2x) + C