#### Answer

a) $x$ = 1852.5 days
b) $x$ = 1531.63 days

#### Work Step by Step

PART A
i) The z-score that corresponds to 80% is 0.84
ii) Solve $z = \frac{x-\mu}{\sigma}$ for $x$ using $\sigma$ =212.5 and $\mu$ = 1674:
$z = \frac{x-\mu}{\sigma}$
$x$ = $\mu$ + $z\sigma$
$x$ = 1674 + (0.84 x 212.5)
$x$ = 1852.5 days
PART B
i) The z-score that corresponds to 25% is -0.67
ii) Solve $z = \frac{x-\mu}{\sigma}$ for $x$ using $\sigma$ =212.5 and $\mu$ = 1674:
$z = \frac{x-\mu}{\sigma}$
$x$ = $\mu$ + $z\sigma$
$x$ = 1674 + (-0.67 x 212.5)
$x$ = 1531.63 days