# Module 0 - Entry Exam v6.0

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Exam contains 69 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.

A biased coin has the following probability distribution function:

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

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.

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

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.

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

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

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

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

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

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

Integrate: A) B) C) D) • A. Option A
• B. Option B
• C. Option C
• D. Option D

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

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

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