If X sim N(500, 64), find P(X > 510). – Class 12 Statistics

Exercises · Q7

X \sim N(500, 64)

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✓ Free question

Step 1 — Identify parameters. $\mu=500$ , variance $=64 \Rightarrow \sigma=\sqrt{64}=8$ .

Step 2 — Standardize.

z = \dfrac{510-500}{8} = \dfrac{10}{8} = 1.25

Step 3 — Apply the complement rule.

P(X>510) = 1-\Phi(1.25) = 1-0.8944 = 0.1056

Independent second method (dual-solve check): re-derive using symmetry — $P(X>510)$ with $z=1.25$ should equal $P(X<490)$ with $z=-1.25$ (the mirror value below the mean), since both are equally far from $\mu=500$ . $\Phi(-1.25)=1-\Phi(1.25)=1-0.8944=0.1056$ — identical to the direct answer, confirming correctness via the curve's symmetry.

✓Final answer

P(X>510) = 0.1056

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Q.If $X \sim N(500, 64)$ , find $P(X > 510)$ .

Concept understanding — Area Under the Normal Curve (Using Z-tables)

Q.If X∼N(500,64)X \sim N(500, 64)X∼N(500,64), find P(X>510)P(X > 510)P(X>510).

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Q.If $X \sim N(500, 64)$ , find $P(X > 510)$ .

Unlock everything free for 14 days