TMUA Statistics 5

Question 1

A linear regression model gives ŷ = 3 + 2x. For x = 5, the observed value is y = 14. What is the residual?

Accepted Answer

1

Answer

Predicted value ŷ = 3 + 2(5) = 13; residual = observed − predicted = 14 − 13 = 1.

Question 2

A fair six-sided die is rolled. Given that the result is even, what is the probability it is greater than 4?

Accepted Answer

1/3

Answer

Even outcomes are {2, 4, 6}; of these, outcomes greater than 4 are {6}, giving P = 1/3.

Question 3

A frequency distribution has class intervals of width 5. The frequency for the interval [20, 25) is 12 and the total frequency is 60. What is the relative frequency for that class?

Accepted Answer

0.20

Answer

Relative frequency = frequency / total = 12/60 = 0.20.

Question 4

X ~ N(μ, σ²). If Z = (X − μ)/σ, which distribution does Z follow?

Accepted Answer

N(0, 1)

Answer

Standardizing a normal variable by subtracting its mean and dividing by its standard deviation produces a standard normal Z ~ N(0,1).

Question 5

The cumulative distribution function (CDF) of a random variable X gives F(x). Which statement correctly describes F(x)?

Accepted Answer

F(x) = P(X ≤ x)

Answer

By definition, the CDF F(x) gives the probability that the random variable X takes a value less than or equal to x.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Statistics 5