The problem asks us to find the value of $P$, where $P = -(U) - BUL$. The given information seems to be related to a statistical analysis, with values for $\bar{X}$, $S$, and a table containing $U_{i-1}$, $\alpha_i$, $\bar{X}$, $\Phi(U_{i-1})$ and $BUL$. We have the values for $\bar{X}=83.09$ and $S=6.72$. We need to deduce how to use the given table to calculate the value of $P$. Since the problem asks us to "find $P, -(U) - BUL)$", it suggests we have to compute the term $-(U) - BUL$ from the given table and that the result should be $P$. We'll assume we need to find the sum of $\Phi(U_{i-1})$ values from the table to find $U$, and the sum of the values in the 5th column, which represents $\Phi(U_{i-1})$, to find $BUL$.

1. Problem Description

The problem asks us to find the value of $P$, where $P = -(U) - BUL$. The given information seems to be related to a statistical analysis, with values for $\bar{X}$, $S$, and a table containing $U_{i-1}$, $\alpha_i$, $\bar{X}$, $\Phi(U_{i-1})$ and $BUL$. We have the values for $\bar{X}=83.09$ and $S=6.72$. We need to deduce how to use the given table to calculate the value of $P$. Since the problem asks us to "find $P, -(U) - BUL)$", it suggests we have to compute the term $-(U) - BUL$ from the given table and that the result should be $P$. We'll assume we need to find the sum of $\Phi(U_{i-1})$ values from the table to find $U$, and the sum of the values in the 5th column, which represents $\Phi(U_{i-1})$, to find $BUL$.

2. Solution Steps

First, we need to find the sum of the values in the $\Phi(U_{i-1})$ column. We must be careful with the signs.

Sum of $\Phi(U_{i-1})$ = $-0.4982 -0.4881 -0.4573 +0.3830 -0.12422 -0.0478 +0.11628 +0.13289$

Sum of $\Phi(U_{i-1})$ = $-0.4982 -0.4881 -0.4573 +0.3830 -0.12422 -0.0478 +0.11628 +0.13289 = -0.98355$

Let $U$ be the sum of values in the $\Phi(U_{i-1})$ column. Thus, $U = -0.98355$

Now, we need to find the sum of values in the column represented as 'S', which from the image is likely to be used to find $BUL$.

$BUL = 3 + 3 + 8 + 39 + 22 + 10 + 3 + 2 = 90$

Now we can calculate $P = -(U) - BUL$

$P = -(-0.98355) - 90$

$P = 0.98355 - 90$

$P = -89.01645$

3. Final Answer

$P = -89.01645$