Respuesta :
The set of parameters that would give you the highest position within the class with a score of x = 75 is option (C) μ = 60 and σ = 5 is the correct answer.
In this question,
A z-score tells us how many standard deviations away a value is from the mean. A positive z-score indicates the raw score is higher than the mean average. A negative z-score reveals the raw score is below the mean average.
According to the Percentile to z-score calculator, the z-score that corresponds to the 90th percentile is 1.2816. Thus, any student who receives a z-score greater than 1.2816 would be considered a “good” z-score.
The options for this question are a) μ = 70 and σ = 5, b) μ = 70 and σ = 10, c) μ = 60 and σ = 5, d) μ = 60 and σ = 10.
The z-score can be calculated as
z-score = [tex]\frac{x-\mu}{\sigma}[/tex]
On substituting the above options of μ and σ with the score of x = 75,
a) μ = 70 and σ = 5,
z-score = [tex]\frac{75-70}{5}[/tex]
⇒ [tex]\frac{5}{5}[/tex] = 1
b) μ = 70 and σ = 10,
z-score = [tex]\frac{75-70}{10}[/tex]
⇒ [tex]\frac{5}{10}[/tex] = 0.5
c) μ = 60 and σ = 5,
z-score = [tex]\frac{75-60}{5}[/tex]
⇒ [tex]\frac{15}{5}[/tex] = 3
d) μ = 60 and σ = 10
z-score = [tex]\frac{75-60}{10}[/tex]
⇒ [tex]\frac{15}{10}[/tex] = 1.5
Thus the z-score 3, is the higher value. 99% have a z-score between -3 and 3. Therefore, the set of parameters that would give you the highest position within the class with a score of x = 75 is option (C) μ = 60 and σ = 5 is the correct answer.
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