NZ Level 8 (NZC) Level 3 (NCEA) [In development] Standardisation and quantiles

## Interactive practice questions

Dylan scored $90%$90% with a $z$z-score of $2$2 in English, and $78%$78% with a $z$z-score of $4$4 in mathematics.

In which subject was his performance better, relative to the rest of his class?

English

A

Mathematics

B

English

A

Mathematics

B
Easy
Less than a minute

If Dave scores $96$96 in a test that has a mean score of $128$128 and a standard deviation of $16$16, what is his $z$z-score?

If Sean's $z$z-score in a test is $-1.1$1.1, the mean mark is $76%$76% and standard deviation is $3%$3%, what is his test score, $X$X?

Kathleen scored $83.4$83.4 in her Biology exam, in which the mean score and standard deviation were $81$81 and $2$2 respectively. She also scored $60$60 in her Geography exam, in which the mean score was $46$46 and the standard deviation was $4$4.

### Outcomes

#### S8-4

Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal

#### 91586

Apply probability distributions in solving problems