 New Zealand
Level 8 - NCEA Level 3

Linear change of scale and origin

Interactive practice questions

A weather station records temperatures normally distributed with a mean of $28$28$^{\circ}$C and a standard deviation of $3.3$3.3$^{\circ}$C.

The temperatures were converted to Kelvin using the rule $Y=X+273.15$Y=X+273.15 where $X$X is the temperature in Celsius and $Y$Y is the temperature in Kelvin.

a

State the new mean.

b

State the new standard deviation.

Easy
Approx 2 minutes

The heights of a certain species of fully grown plants are thought to be normally distributed with a mean of $55$55 cm and a standard deviation of $4$4 cm.

If the heights were recorded in mm instead of cm:

The weights of babies born in a hospital in Sydney are considered normally distributed with a mean of $3.5$3.5 kg and a standard deviation of $0.55$0.55 kg.

If the weights were recorded in grams instead of in kilograms:

In a given population, a certain variable $X$X is considered to be normally distributed with a mean of $300$300 and a standard deviation of $18$18.

If the data for $X$X is transformed according to the rule $3X-3$3X3:

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