The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=540 and standard deviation σ=25.3 (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 35 students who took the test.   (b) What are the mean and standard deviation of the sample mean score 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 546? ANSWER:      (d) What is the probability that the mean score x¯of these students is 546 or higher?

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The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=540 and standard deviation σ=25.3

(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 35 students who took the test.

 

(b) What are the mean and standard deviation of the sample mean score 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 546?
ANSWER: 

 

 

(d) What is the probability that the mean score x¯of these students is 546 or higher?

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