91影视

Regarding exercise 2.86,the distribution of forecast errors from buy-side analysts follows a normal distribution with a mean of 0.85 and a standard deviation of 1.93. The distribution of forecast errors from sell-side analysts follows a normal distribution with a mean of -0.05 and a standard deviation of 0.85.

$x鈥�鈥�~鈥�鈥�N\left(渭,{蟽}^2\right)$where$渭=0.85鈥�鈥�鈥�and鈥�鈥�鈥�蟽=1.93$

$x=2$

The z-score is,

$\begin{array}{rcl}z& =& \frac{x-渭}{蟽}\\ & =& \frac{2-0.85}{1.93}\\ & =& 0.595855\\ & 鈮�& 0.6\\ & & \end{array}$

$\begin{array}{rcl}P\left(x猢�2\right)& =& \left(1-P\left(x<2\right)\right)\\ & =& \left(1-P\left(z<0.6\right)\right)\\ & =& 1-0.7257\\ & =& 0.2743\\ & & \end{array}$

$P\left(x猢�2\right)=0.2743$

Therefore, the probability that a buy-side analyst has a forecast error of +2.00 or higher is0.2743.

$x鈥�鈥�~鈥�鈥�N\left(渭,{蟽}^2\right)$where$渭=-0.05鈥�鈥�鈥�and鈥�鈥�鈥�蟽=0.85$

$x=2$

The z-score is,

$\begin{array}{rcl}z& =& \frac{x-渭}{蟽}\\ & =& \frac{2-\left(-0.05\right)}{0.85}\\ & =& \frac{2.05}{0.85}\\ & =& 2.411765\\ & 鈮�& 2.41\\ & & \end{array}$

$\begin{array}{rcl}P\left(x猢�2\right)& =& \left(1-P\left(x<2\right)\right)\\ & =& \left(1-P\left(z<2.41\right)\right)\\ & =& 1-0.9920\\ & =& 0.008\\ & & \end{array}$

$P\left(x猢�2\right)=0.008$

Therefore, the probability that a sell-side analyst has a forecast error of +2.00 or higher is 0.008.