A Geologist Has Collected 10 Specimens of Basaltic Rock and 10

Question

Examlex · Accepted Answer

The Answer is a. Possible values of X are 5,6,7,8,9,10. (In order to have less than 5 of the granite, there would have to be more than 10 of the basaltic).

P ( X = 5 ) = h ( 5 ; 15,10,20 ) = \frac { \left( \begin{array} { l } 10 \5\end{array} ight) \left( \begin{array} { l } 10 \10\end{array} ight) } { \left( \begin{array} { l } 20 \15\end{array} ight) } = .0163

Following the same pattern for the other values, we arrive at the pmf, in table form below.

\begin{array} { l c c c c c c } \hline x & 5 & 6 & 7 & 8 & 9 & 10 \\hline P ( x ) & .0163 & .1354 & .3483 & .3483 & .1354 & .0163 \\hline\end{array}

b. P(all 10 of one kind or the other) = P(X = 5) + P(X = 10) = .0163 + .0163 + .0326
c. E(X) = n . ( M / N) = 15 (10 / 20) = 7.5;
V(X) = (5/19) (7.5) [1 - (10/20)] = .9869;

\sigma _ { x }

= .9934

\mu \pm \sigma =

7.5

\pm

.9934 = (6.5066, 8.4934), so we want
P( X = 7) + P( X = 8) = .3483 + .3483 = .6966

A Geologist Has Collected 10 Specimens of Basaltic Rock and 10

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