Question

X is a normally distributed random variable with a standard deviation of 4.00. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 13.56

Answer 1

\[
P{ x > 13.56] = .1271
P[ X < 13.56] = 1- .1271=0.8729
\]

Answer 2

12.3

10.3

9.0

8.5
these are my choices

Answer 3

\[
P{ x > 13.56] = .1271\\
P[ X < 13.56] = 1- .1271=0.8729\\
\]

Answer 4

(13.56 - mean)/4 = 1.15
mean =8.96
So 9 is the answer

Answer 5

thank you so much

Answer 6

yw

Answer 7

@eliassaab The population mean cannot be a lower value than 13.56. Therefore none of the proposed choices is correct.

Answer 8

Why?

Answer 9

@kropot72
\[
\int_{13.56}^{\infty } \frac{e^{-\frac{1}{32} (x-9)^2}}{4 \sqrt{2 \pi }} \, dx=0.12714
\]
Try it on any numerical integration system.

Answer 10

Copy and paste on your browser
http://www.wolframalpha.com/input/?i=Integrate [E^%28-%281%2F32%29+%28-9+%2B+x%29^2%29%2F%28++4+Sqrt[2+\[Pi]]%29%2C+{x%2C+13.56%2C+\[Infinity]}]

Answer 11

@kropot72, may be you did not notice that the problem stated the area to the right of 13.56