The scores of students on the SAT college entrance examinationsat a certain high school had a normal distribution with meanμ=542.7 and standard deviation σ=29.8.
(a) What is the probability that a single student randomlychosen from all those taking the test scores 546 or higher?
ANSWER:Â Â
For parts (b) through (d), consider a simple random sample (SRS) of35 students who took the test.
(b) What are the mean and standard deviation of the sample meanscore x¯, of 35 students?
The mean of the sampling distribution for x¯is: Â
The standard deviation of the sampling distribution for x¯ is:
(c) What z-score corresponds to the mean score x¯ of 546?
ANSWER:
(d) What is the probability that the mean score x¯ of thesestudents is 546 or higher?
ANSWER:Â Â
