Respuesta :
Answer:
a) Grade = 93, Standard score = 1.5
Grade = 62, Standard score = -1.6
b) Standard scores = 0.6, Grade = 84
Standard scores = 1.2, Grade = 90
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 78
Standard Deviation, σ = 10
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) Grade = 93
[tex]\text{Standard score } = \displaystyle\frac{93-78}{10} = 1.5[/tex]
Grade = 62
[tex]\text{Standard score } = \displaystyle\frac{62-78}{10} = -1.6[/tex]
b) We have to find grades of student
Standard scores = 0.6
[tex]\displaystyle\frac{x-78}{10} = 0.6\\\\x = (0.6)(10)+78 \\x = 84[/tex]
Grade = 84
Standard scores = 1.2
[tex]\displaystyle\frac{x-78}{10} = 1.2\\\\x = (1.2)(10)+78 \\x = 90[/tex]
Grade = 90
The grade = 93, Standard score = 1.5,grade = 62,
Standard score = -1.6,Standard scores = 0.6, Grade = 84 and Standard scores = 1.2,
Grade = 90
We have given that,Mean( μ )= 78,Standard Deviation(σ) = 10
What is the formula Z score?
[tex]Z=\frac{x-\mu }{\sigma }[/tex]
a) Grade = 93
[tex]slandered score=\frac{93-78}{10} =1.5[/tex]
Grade = 62
[tex]slandered score=\frac{63-78}{10} =-1.6[/tex]
b) We have to find grades of student
Standard scores = 0.6
[tex]\frac{x-78}{10}=0.6[/tex]
[tex]x=(0.6)(10)+78[/tex]
Grade = 84
Standard scores = 1.2
[tex]\frac{x-78}{10}=1.2[/tex]
[tex]x=(1.2)(10)+78[/tex]
x=90
Grade = 90
Therefore we get the grade = 93, standard score = 1.5,grade = 62, Standard score = -1.6,Standard scores = 0.6, Grade = 84 and standard scores = 1.2, Grade = 90
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