Step 1: The scores of high school seniors on the ACT college entrance examinatio

Question

Step 1: The scores of high school seniors on the ACT college entrance examination in a recent year had mean H 22.3 and standard deviation a 5.2 The distribution of scores is only roughly Normal. What is the approximate probability that a single student randomly chosen from all those taking the test scores 27 or higher? The approximate probability is eBook Step 2: The scores of high school seniors on the ACT college entrance examination in a recent year had mean H 22.3 and standard deviation o 5.2 The distribution of scores is only roughly Normal. Now consider an SRS of 4 students who took the test. What are the mean and standard deviation of the sample mean score of these 4 students? Fill in the blanks (give exact answers): 1) The mean is: (Give your answer to 1 decimal place) 2) The standard deviation is (Give your answer to 1 decimal place) Answer 1 Answer 2

Explanation / Answer

6)P(X>27)=1-P(X<27)=1-P(Z<(27-22.3)/5.2)=1-P(Z<0.9038)=1-0.8170=0.1830

2)mean =22.3

std deviation =5.2/(4)1/2=2.6

3)P(X>27)=1-P(Z<(27-22.3)/2.6)=1-P(Z<1.8077)=1-0.9649=0.0351

4)option 4 is correct

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