TMUA Statistics 3

Question 1

A continuous random variable X has PDF f(x) = kx for 0 ≤ x ≤ 4, and 0 otherwise. What is the value of k?

Accepted Answer

1/8

Answer

Integrating kx from 0 to 4 gives 8k = 1, so k = 1/8.

Question 2

Heights of a population are normally distributed with mean 170 cm and standard deviation 8 cm. What proportion of individuals are taller than 186 cm?

Accepted Answer

0.0228

Answer

186 cm is 2 standard deviations above the mean; P(Z > 2) ≈ 0.0228.

Question 3

A hypothesis test uses H₀: μ = 100 vs H₁: μ > 100 with significance level α = 0.05. The test statistic is z = 1.60. What is the correct conclusion?

Accepted Answer

Fail to reject H₀ because z < 1.645

Answer

For a one-tailed test at α = 0.05, the critical value is z = 1.645; since 1.60 < 1.645, we fail to reject H₀.

Question 4

Which of the following correctly describes the relationship between variance and standard deviation?

Accepted Answer

Variance = (Standard deviation)²

Answer

By definition, variance = σ² and standard deviation σ = √(variance), so variance = (standard deviation)².

Question 5

A box contains 5 red, 3 blue, and 2 green balls. Two balls are drawn without replacement. What is the probability that both are red?

Accepted Answer

2/9

Answer

P(both red) = (5/10)×(4/9) = 20/90 = 2/9.

(TMUA) Test of Mathematics for University Admission Practice Test