The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean $\mu = 536.1$ and standard deviation $\sigma = 27.9$.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 543 or higher?
ANSWER:

For parts (b) through (d), consider a simple random sample (SRS) of 25 students who took the test.

(b) What are the mean and standard deviation of the sample mean score $\bar x$, of 25 students?
The mean of the sampling distribution for $\bar x$ is:
The standard deviation of the sampling distribution for $\bar x$ is:

(c) What z-score corresponds to the mean score $\bar x$ of 543?
ANSWER:

(d) What is the probability that the mean score $\bar x$ of these students is 543 or higher?
ANSWER: