Question 1200427
**1. Define the parameters:**

* **p:** Probability of recovery = 0.4
* **n:** Number of people stricken with the disease = 35

**2. Calculate the mean and standard deviation:**

* **Mean (μ):** μ = n * p = 35 * 0.4 = 14
* **Standard deviation (σ):** σ = √(n * p * (1 - p)) = √(35 * 0.4 * 0.6) ≈ 2.898

**3. (a) Probability of 25 or more recovering:**

* **Continuity correction:** Since we're using the normal approximation to the binomial distribution, we need to apply a continuity correction. For "25 or more," we'll use 24.5 as the lower bound.

* **Calculate the z-score:**
   z = (X - μ) / σ = (24.5 - 14) / 2.898 ≈ 3.62

* **Find the probability:** 
   Using a standard normal distribution table or calculator, we find the area to the right of z = 3.62. 
   P(X ≥ 25) ≈ 0.00015

**4. (b) Probability of fewer than 5 recovering:**

* **Continuity correction:** For "fewer than 5," we'll use 4.5 as the upper bound.

* **Calculate the z-score:**
   z = (X - μ) / σ = (4.5 - 14) / 2.898 ≈ -3.28

* **Find the probability:**
   Using a standard normal distribution table or calculator, we find the area to the left of z = -3.28. 
   P(X < 5) ≈ 0.0005

**Therefore:**

* (a) The probability that 25 or more people will recover is approximately **0.00015 (or 0.015%)**.
* (b) The probability that fewer than 5 people will recover is approximately **0.0005 (or 0.05%)**.

**Note:** These probabilities are based on the normal approximation to the binomial distribution. For a more precise calculation, you could use the binomial probability formula directly.