Answer:
Mean = 78.2
Standard deviation = 5.8
Step-by-step explanation:
Mathematically z-score;
= (x-mean)/SD
From the question;
12% of test scores were above 85
Thus;
P( x > 85) = 12%
P(x > 85) = 0.12
Now let’s get the z-score that has a probability of 0.12
This can be obtained from the standard normal distribution table and it is = 1.175
Thus;
1.175 = (85 - mean)/SD
let’s call the mean a and the SD b
1.175 = (85-a)/b
1.175b = 85 - a
a = 85 - 1.175b ••••••••(i)
Secondly 8% of scores were below 70
Let’s find the z-score corresponding to this proportion;
We use the standard normal distribution table as usual;
P( x < 70) = 0.08
z-score = -1.405
Thus;
-1.405 =( 70-a)/b
-1.405b = 70-a
a = 70 + 1.405b ••••••(ii)
Equate the two a
70 + 1.405b = 85 - 1.175b
85 -70 = 1.405b + 1.175b
15 = 2.58b
b = 15/2.58
b = 5.81
a = 70 + 1.405b
a = 70 + 1.405(5.81)
a = 78.16
So mean = 78.2 and Standard deviation is 5.8
B) two real roots is the answer because it is bigger than 0.
De acuerdo con un sistema de ecuaciones, tiene-se que los números son 31 y 84.
----------------
- En el sistema de ecuaciones, tiene-se que los números son x e y.
- Suma de 115, o sea,
- <u>El número mayor es dos veces más 22 unidades que el otro</u>, o sea,
----------------
Primero se encuenta el número menor, <u>reemplazando la segunda ecuación en la primera:</u>
----------------
El número mayor es dado en <u>función de el menor</u>, o sea:
Los números son 31 y 84.
Otro problema resuelto por sistema de ecuaciones es dado en brainly.com/question/24637096
