The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=542.2 and standard deviation σ=28.2 Round z-scores to 2 decimal places...

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=542.2 and standard deviation σ=28.2 Round z-scores to 2 decimal places and give probabilities to 4 decimal places.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 548 or higher?
ANSWER:

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯x¯, of 35 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 548?
ANSWER:

(d) What is the probability that the mean score x¯ of these students is 548 or higher?
ANSWER: