The scores of students on the SAT college entrance examinati

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean ?=539.9 and standard deviation ?=28.5 .

(a) What is the probability that a single student randomly chosen from all those taking the test scores 546 or higher?
ANSWER: ____________

For parts (b) through (d), consider a simple random sample (SRS) of 30 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x

Solution

a)

P( X > = 546) = P( Z > = 546 - 539.9/28.5)

= P(Z >= 0.21403)

= 0.4153

b)

mean = 539.9

standard deviation = 28.5/sqrt(30) = 5.2034

Z-score = 546 - 539.9/5.2034

= 1.1723