Module 0 - Entry Exam v6.0

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Exam contains 64 questions

For the following data set, calculate the mean and median.
10, 8, 5, 7, 14, 5, 3, 9, 5, 8

  • A. The mean is 7.4 and the median is 7.5.
  • B. The mean is 7.4 and the median is 8.0.
  • C. The mean is 8.2 and the median is 7.5.
  • D. The mean is 8.2 and the median is 8.0.


Answer : A

A biased coin has the following probability distribution function:

P(heads) = 0.80 -

P(tails) = 0.20 -
The biased coin is tossed twice in succession.
Calculate the probability of tossing at least one tail.

  • A. 0.20
  • B. 0.36
  • C. 0.64
  • D. 0.80


Answer : B

State what the limit of a function with input variable x represents.

  • A. The limit represents the smallest value that the function can take over its considered range.
  • B. The limit represents the behaviour of a function as x approaches a certain value.
  • C. The limit represents the value of x for which the function is incalculable.
  • D. The limit represents the value of the function when x=0.


Answer : B

In a small island nation, local sea vessels are identified using "a letter and 4 digits" classification system. The "letter" can be any of the 26 letters in the English alphabet, A to
Z, while the "digit" can be any number from 0 to 9. E.g: Z9835.
Calculate the probability of a sea vessel having an identification ending in "007".

  • A. 0.001
  • B. 0.002
  • C. 0.003
  • D. 0.504


Answer : A

Identify the meaning of: | x | > 5

  • A. x is greater than 5.
  • B. x is greater than or equal to 5.
  • C. x is greater than 5 or x is less than -5.
  • D. x is greater than or equal to 5, or x is less than or equal to -5.


Answer : C

The probability density function f(x) for a random variable X is defined over the interval 0 to
1.
f(x) = 2(1-x).
Calculate the probability that X is greater than 0.5.

  • A. 0.25
  • B. 0.5
  • C. 0.75
  • D. 1


Answer : A

Calculate -


  • A. -245
  • B. -95
  • C. -55
  • D. 55


Answer : C

v = f(x, y, z) is a real valued function of 3 variables.
Express the partial derivative of v with respect to z in standard mathematical notation.
A)


B)

C)

D)

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D


Answer : B

Using simple iteration, based on trial and improvement, the cubic equation below can be solved:
2x3 + 5x2 +7x - 12 = 0
Solve for x to 6 decimal places.

  • A. 0.909000
  • B. 0.909165
  • C. 0.909502
  • D. 1.000000


Answer : B

For random variable X, use the following statistics to calculate its coefficient of skewness based on central moments.

E(X) = 3.940 -

E(X2) = 21.466 -
skew(X) = E[(X - )3] = 6.008

  • A. -0.415
  • B. 0.060
  • C. 0.415
  • D. 0.768


Answer : C

Calculate which of the following is a simplification of (1 + x)2 - x2 + ln(e3x).

  • A. 1 + 2x
  • B. 1 + 3x
  • C. 1 + 5x
  • D. 1 + 2x + x3


Answer : C

Integrate:


A)

B)

C)

D)

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D


Answer : C

Determine which of the statements is true about the root(s) of the following equation:


  • A. There is only one real root which takes a positive value.
  • B. There is only one real root which takes a negative value.
  • C. There are two real roots, r1 and r2, where r1 is positive and:r1 = - 0.5 r2
  • D. There are two real roots, r1 and r2, where r1 is positive and:r1 = - 2 r2


Answer : C

The graph shows the frequency distribution of the age of people with a certain kind of insurance contract.


Describe the shape of the underlying data.

  • A. Negatively skewed
  • B. Positively skewed
  • C. Symmetric
  • D. Symmetric about the mean


Answer : A

Three light bulbs are chosen at random from 15 bulbs of which 5 are known to be defective.
Calculate the probability that exactly one of the three is defective.
A)


B)

C)

D)

  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D


Answer : C

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Exam contains 64 questions

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