Question

Suppose that scores on a knowledge test are normally distributed with a mean of 60 anda standard deviation of 4.3. Scores on an aptitude test are normally distributed with a mean of 110 and a standard deviation of 7.1 Boris scored a 67 on the knowledge test and Callie scored 119 on the aptitude test. (a) Calculate the z-score for Boris. Round to the nearest hundredth. Show your work (b) Calculate the z-score for Callie. Round to the nearest hundredth. Show your work. (c) Who did relatively better on their test, Boris or Callie? Use the meaning of z-scores to explain​

Answer 1

The Z-score for Boris is 1.627, and the Z-score value for the Callie is 1.267, Boris scored higher relatively.

What is Z-test?

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

We know the formula for the Z-test:

[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]

(a) For Boris:

[tex]\rm Z = \dfrac{67-60}{4.3}[/tex]

Z = 1.627

(b) For Callie:

[tex]\rm Z = \dfrac{119-110}{7.1}[/tex]

Z = 1.267

(c) Since the measures of two different data have been set to one measure and the value of the Z-score for Boris is higher relative to the Z-score value of Callie so Boris scored higher relatively.

Thus, the Z-score for Boris is 1.627, and the Z-score value for the Callie is 1.267, Boris scored higher relatively.

Learn more about the Z-test here:

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