Question 1174398
**1. Calculate the Standard Error:**

* The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the mean.
* SEM = σ / √n 
   where:
     * σ = population standard deviation ($3712)
     * n = sample size (75)
* SEM = 3712 / √75 ≈ 428.3193

**2. Calculate the z-score:**

* The z-score measures how many standard errors the sample mean is away from the population mean.
* z = (x̄ - μ) / SEM
   where:
     * x̄ = sample mean ($24,000)
     * μ = population mean ($24,260)
     * SEM = standard error of the mean (428.3193)
* z = (24000 - 24260) / 428.3193 ≈ -0.6070

**3. Find the Probability:**

* We want to find the probability that the sample mean is $24,000 or less, which is equivalent to finding the area to the left of the z-score of -0.6070 in the standard normal distribution.
* Using a z-table or calculator, we find that the probability is approximately 0.272.

**Therefore, the probability that the mean salary offer for these 75 students is $24,000 or less is approximately 0.272.**