SOLUTION: Two standardized​ tests, test A and test​ B, use very different scales. Assume that in one year the distribution of scores on test A can be modeled by N(1100,25)and scores on t
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Question 1197495: Two standardized​ tests, test A and test​ B, use very different scales. Assume that in one year the distribution of scores on test A can be modeled by N(1100,25)and scores on test B can be modeled by N(11,2) . If an applicant to a university has taken test A and scored 1190 and another student has taken test B and scored 15 ​, compare these​ students' scores using​ z-values. Which one has a higher relative​ score? Explain.
The​ z-value of the test A score is
  
enter your response here.
​(Round to two decimal places as​ needed.)
Part 2
The​ z-value of the test B score is
  
enter your response here.
​(Round to two decimal places as​ needed.)
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Test A's scores are distributed according to N(1100,25)
We have a normal distribution with mean mu = 1100 and standard deviation sigma = 25
The template is N(mu, sigma)
If a person gets a score of x = 1190 on test A, then,
z = (x - mu)/sigma
z = (1190 - 1100)/25
z = 3.6
This person got a score exactly 3.6 standard deviations above the mean.
Test B's scores are distributed by N(11,2)
mu = 11
sigma = 2
If a person scored x = 15 on this test, then,
z = (x - mu)/sigma
z = (15 - 11)/2
z = 2
This person got a score 2 standard deviations above the mean.
We see that the person taking test A did better compared to their peers. By "peers" I mean the people taking the same test.
Answers:
z score for test A: 3.6
z score for test B: 2
Who has a higher relative score? The person who took test A
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