Subjects statistics

Iq Continuity Correction

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

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.