The normal distribution (HSC Maths Standard 2) quiz

For $X \sim N(50, 8^2)$, so mean $50$ and standard deviation $8$, what is the $z$-score of $x = 66$?

For $X \sim N(50, 8^2)$, the value $x$ whose $z$-score is $-1.25$ is found from $x = \mu + z\sigma$. What is $x$?

By the empirical rule, approximately what percentage of a normal distribution lies between $\mu - 2\sigma$ and $\mu + 1\sigma$?

Marks are $N(60, 10^2)$, so mean $60$ and standard deviation $10$. By the empirical rule, about what percentage of students scored above $80$?

For the standard normal $Z \sim N(0, 1)$ with $\Phi(1.2) = 0.8849$, what is $P(Z > 1.2)$?

Adult female heights are $N(162, 7^2)$ cm. Using $\Phi(1.43) = 0.9236$, the proportion of women shorter than $172$ cm is closest to:

Cara scored $74$ on a test with mean $65$ and SD $9$. Dan scored $80$ on a test with mean $72$ and SD $10$. Whose result was better relative to their cohort?

Raw marks are $N(68, 12^2)$. The cut-off raw mark for the top 5% of students, using $z = 1.645$ and $x = \mu + z\sigma$, is closest to:

In a normal distribution, approximately what percentage of values lie above $\mu + 1\sigma$?

Anika scored $76$ on a test with mean $68$ and SD $6$. Her $z$-score is closest to: