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#### karush

##### Well-known member

- Jan 31, 2012

- 2,719

still having trouble figuring this out!

The graph shows a normal curve for the random variable \(\displaystyle X\), with mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\)

It is known that \(\displaystyle P \left(X \geq12 \right) = 0.1\).

(a) The shaded region \(\displaystyle A\) is the region under the curve where \(\displaystyle x \geq 12\). Write down the area of the shaded region \(\displaystyle A\).

It is also known that \(\displaystyle P(X \leq 8) = 0.1\).

(b) Find the value of \(\displaystyle \mu\), explaining your method in full.

in that \(\displaystyle \mu\) is in between 8 and 12 which would be \(\displaystyle \mu=10\)

(c) Show that \(\displaystyle \sigma = 1.56\) to an accuracy of three significant figures.

(d) Find \(\displaystyle P(X \leq 11)\).