Thread: distribution probability
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Old June 30th, 2009, 04:17 PM
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Originally Posted by WillB View Post
I'm sorry. I am using tables to find the values. This is my first post and I am not really sure how this works. I will show you what I did so far.

a.

P(\frac{75-80}{15}\le\frac{x-80}{\sqrt{225}}\le\frac{85-80}{15})=\Phi(0.3)-\Phi(-0.3)=0.6293-0.3707=0.2586

Mr F says: {\color{red} \frac{1}{3} \neq 0.3}. The accuracy of your answer has suffered as a consequence. Since your tables will be 'four figure' maths tables you should at least use {\color{red} \frac{1}{3} = 0.3333} (correct to four decimal places).

b. P(X<50)

\frac{50-80}{15}=-2

\Phi 2=0.9772 (I'm not sure which table to use for >)

1-0.9772=0.0228

Mr F says: Looks OK.

c. P(X>95)

\frac{95-80}{15}=0.33333 Mr F says: Last time I checked, {\color{red}\frac{95-80}{15}= 1}.

1-\Phi 0.33333=1-0.6293=0.3707


d. P(|X-80|>18)

I'm not exactly sure how you did it, but going from your work: Mr F says: I used the symmetry of the normal distribution arund its mean.

2(1-P(X<98)

\frac{98-80}{15}=1.2

\Phi 1.2=0.8849

2(1-0.8849)=0.2302 Mr F says: Looks OK. Note that the calculation is the same as Pr(Z > 1.2) + Pr(Z < -1.2). Perhaps the symmetry is more obvious now ....
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