Final answer:
The national average SAT score is estimated using z-scores from a given standard deviation and probability. A z-score of 1.28 corresponds to the probability of the mean score being greater than 1050 from a sample of 16 students. Calculating the mean gives a value close to 1020, with the closest provided option being 1000.
Step-by-step explanation:
The question involves finding the national average SAT score based on a given standard deviation and the probability related to the mean score of a randomly selected group of students.
We need to use the concept of z-scores in a normal distribution to answer this question. The formula for z-score is:
Z = (X - μ) / (σ / √n)
Where X is the score, μ is the mean, σ is the standard deviation, and n is the sample size.
Here, we are given σ = 92, n = 16, and we know from standard normal distribution tables that a z-score with a probability of 0.10 to the right of it is approximately 1.28.
Thus, we have:
1.28 = (1050 - μ) / (92 / √16)
1.28 = (1050 - μ) / 23
μ = 1050 - (1.28 * 23)
μ = 1050 - 29.44
μ = 1020.56
Since 1020.56 is not one of the provided options, the closest choice, and thus the best answer from the choices given is: A. 1000.