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.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

560

hope this : )