LEARN · EXPLAIN · REVISE

X~N(t,4), Φ(1)=0.8413. Find P(t−2≤X≤t+2).

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

TOPIC 01

Random variables and distributions: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

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

01 / Standard#Your turn

t=29

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.

\Phi(-1)=1-\Phi(1)

Worked solution

Express the event with a conditional probability or a disjoint partition.
Apply the stated relation and retain its conditions.
$P(-1\le Z\le1)=2\Phi(1)-1=0.6826$
Subtract the lower tail rather than adding two cumulative probabilities.

The requested value is 0.6826.

Checks and common pitfalls: Subtract the lower tail rather than adding two cumulative probabilities.

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

Teacher preparation and assessment