WACE Mathematics Methods probability and statistics: exam-style practice quiz

The discrete random variable $X$ takes the values 1, 2, 3 and 4 with probabilities $0.2$, $0.3$, $k$ and $0.1$ respectively. The value of $k$ and $E(X)$ are:

A random variable $X$ has $E(X) = 3$ and $\text{Var}(X) = 2$. If $Y = 4 - 2X$, then:

A bag holds 5 red and 5 blue counters. Four counters are drawn without replacement and $X$ is the number of red counters drawn. Why is a binomial model for $X$ not appropriate?

Section Two style. $X \sim \text{Bin}(12, 0.4)$. $P(X \ge 2)$ is closest to:

A binomial random variable has mean 6 and variance 4.2. Its parameters are:

A continuous random variable has probability density function $f(x) = k(4 - x)$ for $0 \le x \le 4$, and 0 elsewhere. $P(X < 2)$ equals:

A continuous random variable has probability density function $f(x) = \frac{3}{8}x^2$ for $0 \le x \le 2$, and 0 elsewhere. $E(X)$ equals:

A coffee machine dispenses volumes $X \sim N(250, 4^2)$ mL. The proportion of cups with less than 244 mL is closest to:

Section Two style. Delivery times are modelled by $T \sim N(35, 6^2)$ minutes. A company wants to promise delivery within $k$ minutes for 95 percent of orders. The value of $k$ is closest to:

In a large population, 20 percent of people are left-handed. For random samples of 400 people, $P(\hat{p} > 0.24)$ is approximately:

Section Two style. In a random sample of 500 voters, 140 support a proposal. An approximate 95 percent confidence interval for the population proportion is:

A 95 percent confidence interval for a proportion, from a sample of 400, has a margin of error of 0.05. With the sample proportion about the same, roughly what sample size would give a margin of error of 0.025?

A random sample gives a 95 percent confidence interval of $(0.52, 0.60)$ for the proportion of WA Year 12 students with a part-time job. Which interpretation is correct?