For the follow questions please record your answers to at least three decimal places. The scores of students on the SAT college entrance examinations...
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For the follow questions please record your answers to at least three decimal places. 

The scores of

students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=554.9 and standard deviation σ=28.6


(a) What is the probability that a single student randomly chosen from all those taking the test scores 560 or higher? 

ANSWER:  


For parts (b) through (d), consider a simple random sample (SRS) of 25 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x dash of 25 students? 

The mean of the sampling distribution for x dash is :


The standard deviation of the sampling distribution for x dash is :


(c) What z-score corresponds to the mean score x dash of 560? 


ANSWER: 


(d) What is the probability that the mean score x dash of these students is 560 or higher? 

ANSWER:  

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