Question 1174399
**1. Identify the Parameters:**

* Confidence Level: 95%  (This gives us a z-score of 1.96)
* Margin of Error (E): 0.05
* Estimated Population Proportion (p̂): 0.65 (from past polls)
* Estimated Population Proportion who don't approve (q̂) = 1 - p̂ = 0.35

**2. Use the Sample Size Formula:**

The formula for calculating the sample size (n) for estimating a population proportion is:

n = (z^2 * p̂ * q̂) / E^2

**3. Plug in the Values:**

n = (1.96^2 * 0.65 * 0.35) / 0.05^2

**4. Calculate:**

n ≈ 350.28

**5. Round Up:**

Since we cannot have a fraction of a person, always round the sample size up to the nearest whole number.

n = 351

**Therefore, the Dean needs a sample size of 351 students to achieve the desired level of confidence and margin of error.**