LEARN · EXPLAIN · REVISE

Standardise x=t+4 under X~N(t,4). Find z.

Read the idea, work independently, then explain what changed.

高三選擇性必修第三册(A版).pdf · 7.5 · PDF 88 / printed page 83

TOPIC 01

Normal distribution

Standardise a normal variable and interpret supplied table probabilities and symmetry.

Standardise a normal variable and interpret supplied table probabilities and symmetry.
Justify the method and check the conditions in a new situation.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

t=6

σ>0; probability table values are supplied in each task. A continuous variable has zero probability at a single point.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

List the possible values and probabilities before computing moments.

Hint 2

Use this intermediate relation.

z=(x-\mu)/\sigma

Worked solution

The requested value is 2.

Checks and common pitfalls: Divide by standard deviation, not variance.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Standardise a normal variable and interpret supplied table probabilities and symmetry.
Which condition is essential in normal distribution?
Does shifting the mean change the probability within one standard deviation?

Defining relation: Standardise a normal variable and interpret supplied table probabilities and symmetry.
$Z=(X-\mu)/\sigma$
Conditions: σ>0; probability table values are supplied in each task. A continuous variable has zero probability at a single point.