NZ Level 7 (NZC) Level 2 (NCEA)
z-scores (what they are and calculating them)

## Interactive practice questions

The mean of a set of scores is $77$77 and

the standard deviation is $29$29. Find the value of:

a

$\text{Mean }-\text{Standard Deviation}$Mean Standard Deviation

b

$\text{Mean }+2\times\text{Standard Deviation}$Mean +2×Standard Deviation

c

$\text{Mean }-\frac{\left(2\times\text{Standard Deviation}\right)}{3}$Mean (2×Standard Deviation)3

d

$\text{Mean }+\frac{\left(4\times\text{Standard Deviation}\right)}{5}$Mean +(4×Standard Deviation)5

e

$\text{Mean }+3\times\text{Standard Deviation}$Mean +3×Standard Deviation

f

$\text{Mean }-2\times\text{Standard Deviation}$Mean 2×Standard Deviation

Easy
Approx 4 minutes

The mean of a set of scores, denoted by $\mu$μ, is $51$51 and

the standard deviation is $16$16, and is denoted by $\sigma$σ. Find the value of:

The literacy rate of a population is used to help measure the level of development of a country. The average literacy rate in a particular country is $59%$59%, and the standard deviation is $5%$5%. The literacy rate varies from place to place within the country.

The following table shows the marks obtained by a student in two subjects.

### Outcomes

#### S7-4

S7-4 Investigate situations that involve elements of chance: A comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions B calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

#### 91267

Apply probability methods in solving problems