Statistical analysis (Year 12 Maths Advanced) quiz

$\sum p_i x_i$

$\sum x_i$

$\sum p_i$

$\sum x_i^2 p_i$

$(E(X))^2 - E(X^2)$

$E(X^2) - (E(X))^2$

$E(X^2) + (E(X))^2$

$E(X^2) - E(X)$

$0$

$0.25$

$0.5$

$1$

50 percent

95 percent

99.7 percent

68 percent

$0.5$

$1.5$

$2.0$

$15$

$+0.8$

$-1$

$0$

Cannot be determined

Predicting values far outside the observed data range with a high degree of confidence

Determining a definite cause-and-effect relationship between the two variables

Interpolation within the data range, with caution about extrapolation

Smoothing seasonal fluctuations out of a noisy time-series dataset

Mean $0$ and SD $0$

Mean $1$ and SD $0$

Mean $1$ and SD $1$

Mean $0$ and SD $1$

$0.70$

$0.58$

$0.12$

$0.10$

$E(X) = 2$, $\text{Var}(X) = 1$

$E(X) = 2$, $\text{Var}(X) = 4$

$E(X) = 1.5$, $\text{Var}(X) = 2$

$E(X) = 2$, $\text{Var}(X) = 0$

Heights of adult women measured across a large city

The result of a fair coin flip (heads or tails)

IQ scores measured across a very large population

Random measurement errors in a careful chemistry experiment

I am going to start this question by simply finding the mean of all the given numbers first, before I do anything else at all in my working.

Statistics as a topic is basically all about probability and chance, and that is the main idea I will keep in mind throughout this whole question.

First of all, before doing any of the actual calculations at all, I am just going to draw a quick rough graph of all of the given data so that I can see roughly what the overall shape of it looks like.

Let $X$ be the random variable representing daily rainfall. Then $E(X)$ and $\text{Var}(X)$ can be computed from the probability table, after which standardisation lets me find $P(X > x)$.