Question

The results on the Spanish regents were normally distributed with a mean of 82 and a standard
deviation of 2.5. The results on the French regents were normally distributed with a mean of 84
and a standard deviation of 3. If you scored between an 75 and 84 on the Spanish regents, what
would someone need to score on the French regents to do as well as you? (Hint: find the z-scores
for the Spanish regents first!)

Answer 1

Given Mean of Spanish regents s = 82

Standard deviation of Spanish regents s = 2.5

Z-score = (X - ) /

Z-score for 75 is calulated as below

Z-score = (75 - 82) / 2.5

= -7/2.5

= -2.8

Z-score for 84 is calulated as below

Z-score = (84 - 82) / 2.5

= 2/2.5

= 0.8

The z-scores will be same for both the Spanish and French regents sicne we are trying to find the scores where they someone will perfrom as good as you

We will find the two X values for the z-scores for the French regents since we already have the z-scores of the Spanish regents with us

Mean of French regents f = 84

Standard deviation of Spanish regents f = 3

Now for z-score of -2.8, we will find the X value

Z-score = (X - ) /

-2.8 = (X - 84) / 3

X - 84 = 3 * (-2.8)

X = 84 - 8.4

X = 75.6

Now for z-score of 0.8, we will find the X value

Z-score = (X - ) /

0.8 = (X - 84) / 3

X - 84 = 3 * 0.8

X = 84 + 2.4

X = 86.4

  

So If you scored between an 75 and 84 on the Spanish regents, then someone need to score between 75.6 and 86.4 on the French regents to do as well as you