test a and test b\nuse the information below to answer the questions:\nintelligence quotas on two different…
test a and test b\nuse the information below to answer the questions:\nintelligence quotas on two different tests are normally\ndistributed. test a has a mean of 100 and a standard deviation of\n15. test b has a mean of 100 and a standard deviation of\n16. use z - scores to determine which person has the higher\niq: person a who scores 125 on test a, or person b who scores\n124 on test b.\npart a\nwhat is the z - score for test a?\nround your answer to two decimal points.\npart b\nwhat is the z - score for test b?\npart c\nwhich individual has the higher iq?
Answer
Explanation:
Part A: Calculate z - score for Test A
Step1: Recall the z - score formula
The z - score formula is (z=\frac{x-\mu}{\sigma}), where (x) is the raw score, (\mu) is the mean, and (\sigma) is the standard deviation. For Test A, (x = 125), (\mu=100), (\sigma = 15).
Step2: Substitute values into the formula
(z_A=\frac{125 - 100}{15}=\frac{25}{15}\approx1.67)
Part B: Calculate z - score for Test B
Step1: Use the z - score formula
For Test B, (x = 124), (\mu = 100), (\sigma=16)
Step2: Substitute values
(z_B=\frac{124 - 100}{16}=\frac{24}{16}=1.50)
Part C: Compare z - scores
Step1: Analyze the z - scores
Since (z_A\approx1.67) and (z_B = 1.50), and a higher z - score indicates a relatively higher score within the distribution.
Answer:
- Part A: (1.67)
- Part B: (1.50)
- Part C: Person A