The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=559.1μ=559.1 and standard deviation σ=26.2σ=26.2.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 565 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¯x¯ is: 
The standard deviation of the sampling distribution for x¯x¯ is: 

(c) What z-score corresponds to the mean score x¯x¯ of 565?
ANSWER: 

(d) What is the probability that the mean score x¯x¯ of these students is 565 or higher?
ANSWER: 

EstimatingMeans: