Name Problem #3 Entry to a certain University is determined by a national test.
ID: 2927765 • Letter: N
Question
Name Problem #3 Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. (a) A certain student wants to be admitted to this university and he knows that he must score 85 better than at least 70% of the students who took the test. He takes the test and scores 5 Will he be admitted to this university? (b) The university receives 1000 total applicants. One particular student scores 912 on the standardized test. One member of the faculty performs a statistical analysis and determines that this student is an alien (i.e, the student is not part of the distribution of humans taking the test). Is the faculty member's analysis correct?Explanation / Answer
a)for 70th percentile ; z score =0.5244
therefore corresponding score for above 70th percentile =mean+z*std deviaiton =500+0.5244*100=552.44
as score of 585 is higher then 70th percentile ; therfore he must be admitted
b) as probability of scoring aq score of 912 or above =P(X>912) =1-P(X<912)=1-P(Z<(912-500)/100)
=1-P(Z<4.12)=1-0.99998 =0.00002
as probability of that happening is very low ; we can see that it is an extraordinary score and the person can be categorized into the topmost category different from other students, therefore member analysis is correct
please revert for any explanation required,
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