LEARN · EXPLAIN · REVISE

X~N(t,9), Φ(2)=0.9772. Find P(X>t+6).

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 / Standard#Your turn

t=10

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

Express the event with a conditional probability or a disjoint partition.

Hint 2

Use this intermediate relation.

z=6/3=2

Worked solution

Express the event with a conditional probability or a disjoint partition.
Apply the stated relation and retain its conditions.
$P(X>\mu+2\sigma)=1-\Phi(2)=0.0228$
The requested event is a right tail, not a left cumulative probability.

The requested value is 0.0228.

Checks and common pitfalls: The requested event is a right tail, not a left cumulative probability.

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.