Answer-
The missing data value is 39.
Solution-
We know that a Z-score is the number of standard deviations from the mean a data point is. Mathematically it is represented as,
[tex]Z=\dfrac{X-\mu}{\sigma }[/tex]
Where,
Z = Z-score or standard score,
X = Raw score,
μ = Mean of the sample
σ = Standard deviation
Here, we are given with
Z-score = -2.1
μ = 43
σ = 2
So the raw score or X is missing here, putting the values in teh formula,
[tex]\Rightarrow -2.1=\dfrac{X-43}{2}[/tex]
[tex]\Rightarrow X-43=-2.1\times 2[/tex]
[tex]\Rightarrow X=-4.2+43[/tex]
[tex]\Rightarrow X=38.8\approx 39[/tex]
Answer: A) 39
Step-by-step explanation:
For any random variable x , the formula to find the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Given : A missing data value from a set of data has a z-score of –2.1.
Fred already calculated the mean and standard deviation to be [tex]\mu=43[/tex] and [tex]\sigma=2[/tex] .
Substitute all the value in the formula , we get
[tex]-2.1=\dfrac{x-43}{2}[/tex]
Multiply 2 both sides , we get
[tex]-4.2=x-43[/tex]
Add 43 on both the sides , we get
[tex]-4.2+43=x[/tex]
Or [tex]x= 38.8\approx39[/tex]
Hence, the missing data value = 39
