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nataliamontirl8152
03.12.2019 •
Mathematics
Test grades on the last statistics exam had a mean = 78 and standard deviation = .14. suppose the teacher decides to curve by subtraction 31 from all scores then doubling the values. if y represents the new test scores, what is the mean and standard deviation of y?
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Ответ:
The mean and standard deviation of Y are, 94 and 0.28 respectively.
Step-by-step explanation:
Let the random variable , 'Test grades on the last statistics exam' be X.
Then according to the question,
E(X) = 78 ------------(1)
and
Now, according to the question,
Y = 2(X - 31)
⇒E(Y) = 2(E(X) - 31)
=![2 \times (78 - 31)](/tpl/images/0401/1761/a58e8.png)
= 94 ----------------(4)
and
V(Y) = 4V(X)
⇒![\sigma_{Y} = 2 \times \sigma_{X}](/tpl/images/0401/1761/1673c.png)
⇒
= 0.28
So, the mean and standard deviation of Y are, 94 and 0.28 respectively.
Ответ: