Question

test a and test b
use the information below to answer the questions:
intelligence quotas on two different tests are normally
distributed. test a has a mean of 100 and a standard deviation of

1. test b has a mean of 100 and a standard deviation of
2. use z - scores to determine which person has the higher

iq: person a who scores 125 on test a, or person b who scores
124 on test b.
part a
what is the z - score for test a?
round your answer to two decimal points.
part b
what is the z - score for test b?
part c
which individual has the higher iq?

Explanation:

Part A: Calculate the 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, \(x = 125\), \(\mu=100\), and \(\sigma = 15\).

Step2: Substitute the values into the formula

\(z_A=\frac{125 - 100}{15}=\frac{25}{15}\approx1.67\)

Part B: Calculate the z - score for Test B

Step1: Use the z - score formula

For Test B, \(x = 124\), \(\mu = 100\), and \(\sigma=16\)

Step2: Substitute the values

\(z_B=\frac{124-100}{16}=\frac{24}{16}=1.50\)

Part C: Compare the 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 position within the distribution.

Answer:

Part A: \(1.67\)
Part B: \(1.50\)
Part C: Person A