Respuesta :
Answer:
The z-score for the value 489.67 is 3.31.
Step-by-step explanation:
If X [tex]\sim[/tex] N (µ, σ²), then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).
The distribution of these z-variate is known as the standard normal distribution.
The information provided is:
μ = 108.06
σ = 115.45
Compute the z-score for the raw score X = 489.67 as follows:
[tex]Z=\frac{X-\mu}{\sigma}=\frac{489.67-108.06}{115.45}=3.3054\approx3.31[/tex]
Thus, the z-score for the value 489.67 is 3.31.
Answer:
z score for a value of 489.67 is 3.31 .
Step-by-step explanation:
We are given that the mean of a set of data is 108.06 and its standard deviation is 115.45.
Let X = Data set ; So, X ~ N([tex]\mu = 108.06,\sigma^{2}=115.45^{2}[/tex])
The z score probability distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
Z score for a value of 489.67 is given by;
Z = [tex]\frac{489.67 - 108.06}{115.45}[/tex]
Z = [tex]\frac{381.61}{115.45}[/tex] = 3.31
Hence, z score for a value of 489.67 is 3.31 .
