Question 1177034
Absolutely! Let's solve this step by step.

**Understanding the Problem**

* **Sample size (n):** 225
* **Sample mean (x̄):** 244.3
* **Population mean (μ):** 245 (This is the mean we're comparing to)
* **Population standard deviation (σ):** 15 (This is the standard deviation of the population)
* **We want to find:** P(x̄ < 244.3)

**Steps to Solve**

1. **Calculate the standard error of the mean (SE):**
   SE = σ / √n
   SE = 15 / √225
   SE = 15 / 15
   SE = 1

2. **Calculate the z-score:**
   z = (x̄ - μ) / SE
   z = (244.3 - 245) / 1
   z = -0.7

3. **Find the probability (P-value):**
   We want to find P(z < -0.7). This is the area under the standard normal distribution curve to the left of z = -0.7.
   Using a z-table or calculator, we find that P(z < -0.7) ≈ 0.2420.

**Answer**

The probability that a sample size of 225 is randomly selected with a mean less than 244.3 is approximately 0.2420.