The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=546.2 and standard deviation σ=25.7.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 553 or higher?


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 x¯, of 25 students?
The mean of the sampling distribution for x¯ is:

The standard deviation of the sampling distribution for x¯ is:
(c) What z-score corresponds to the mean score x¯ of 553?

(d) What is the probability that the mean score x¯ of these students is 553 or higher?