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Normal Distribution

The random variable X~N(μ,σ²).

It is known that
P(X<66)=0.0359 and P(X>81)=0.1151

(a) Draw a clearly labelled sketch to represent these probabilities on a Normal curve.
(b) (i) Show that the value of σ is 5.
(ii) Find the value of μ.
(c) Find P(69<X<83)

So I've done question (a), but I'm not really sure how to go about doing the rest of the question. I think (b) (i) might involve simultaneous equations, but like I said I'm not very sure!

If you check the normal distribution table in your textbook or formula book you will see

P(Z<1.8)=0.9641

\Rightarrow P(Z>1.8)=1-0.9641=0.0359

\Rightarrow P(Z<-1.8)=0.0359

From this we can see that

66=\mu -1.8 \sigma

.

Form another equation in a similar manner.

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