Answer:
X = 40
Step-by-step explanation:
Original mean (µ) = 37
Original standard deviation (σ) = 6
New mean (µ) = 50
New standard deviation (σ) = 10
The z-score of an individual who had a score of X=55 in the new distribution is given by:
[tex]z=\frac{X-\mu}{\sigma}\\z=\frac{55-50}{10}\\z=0.5[/tex]
A z-score of 0.5, in the original distribution yields a score, X, of:
[tex]0.5=\frac{X-37}{6}\\X=0.5*6 +37\\X=40[/tex]
This individual’s score in the original distribution is X = 40
Following are the calculation for the distribution:
Given:
Original value
[tex]\mu=37\\\\\sigma=6[/tex]
New value
[tex]\mu=50\\\\\sigma=10[/tex]
[tex]X=55[/tex]
To find:
original distribution [tex](X)=?[/tex]
Solution:
In the given question, when the z-score is an individual then the [tex]X=55[/tex] so, the new distribution:
[tex]\to Z=\frac{X-\mu}{\sigma}=\frac{55-50}{10}=\frac{5}{10}=0.5[/tex]
Now we using the Z-score value that is 0.5. so, the original distribution of the X score:
[tex]\to 0.5=\frac{X-37}{6}\\\\\to X=0.5 \times 6 +37\\\\\to X=3.0+37\\\\\to X= 40[/tex]
So, the individual’s score for the original distribution of "[tex]X = 40[/tex]".
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