Diana and Michael, who are taking different classes, are arguing about who did better on their most recent test. Diana received a score of 92 on her History test and Michael received a 688 on his Math test. The mean test score for the History class is 71 with a standard deviation of 15.The mean test score for the Math class is 493 standard deviation of 150. Who did better, relative to other students in the same class? Justify your answer.

Diana's score is better.

Step-by-step explanation:

In Diana case :

Score = 92

Mean score , μ = 71

Standard deviation σ = 15

So,

P( x ≥ 92 ) = 1 - P( x ≤ 92 )

                = 1 - P(z ≤ )

                = 1 - P( z ≤ )

                = 1 - P( z ≤ 1.4 )

                = 1 - 0.9192

                = 0.0808 = 8.08 %

⇒P( x ≥ 92 ) = 8.08%

∴ we get

Diana score is > 91.92% other students in the class.

In Micheal case :

Score = 688

Mean score , μ = 493

Standard deviation σ = 150

So,

P( x ≥ 688 ) = 1 - P( x ≤ 688 )

                = 1 - P(z ≤ )

                = 1 - P( z ≤ )

                = 1 - P( z ≤ 1.3 )

                = 1 - 0.9032

                = 0.0968 = 9.68 %

⇒P( x ≥ 688 ) = 9.68%

∴ we get

Micheal score is > 90.32% other students in the class.

From both scores , we can conclude that

Diana's score is better.

yes. we do proportions in probabilities.