The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ = 536.6 and standard deviation σ = 29.1.
(a) What is the probability that a single student is randomly chosen from all those taking the test scores 541 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 x̄, of 35 students?
The mean of the sampling distribution for x̄ is: ____
The standard deviation of the sampling distribution for x̄ is: ____
(c) What z-score corresponds to the mean score x̄ of 541?
ANSWER: _______
(d) What is the probability that the mean score x̄ of these students is 541 or higher?
ANSWER: _______