1. **State the problem:** We want to find how many students have IQs less than 95, given IQs are recorded as integers and applying continuity correction.
2. **Apply continuity correction:** Since IQs are integers, for IQ < 95, we consider values \( \leq 94 \). The continuous cutoff is \( X = 94 + 0.5 = 94.5 \).
3. **Compute the Z-score:** Using mean \( \mu = 115 \) and standard deviation \( \sigma = 12 \),
$$ Z = \frac{X - \mu}{\sigma} = \frac{94.5 - 115}{12} = \frac{-20.5}{12} \approx -1.71 $$
4. **Find the probability:** From standard normal tables or a calculator,
$$ P(Z < -1.71) \approx 0.0436 $$
5. **Calculate the number of rejected students:** Total students = 600,
$$ \text{Rejected} = 0.0436 \times 600 \approx 26.16 \approx 26 $$
**Final answer:** 26 students are rejected.
Iq Continuity Correction
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