Answer
$\mu= 20.8$
$\sigma^2=1.56$
$\sigma=1.249$
$104$ suits.
Work Step by Step
Use the formula for weighted mean, we have
$\mu= (0.2×19+0.2×20+0.3×21+0.2×22+0.1×23) / (0.2+0.2+0.3+0.2+0.1) = 20.8$
Use the formula for weighted variance, we have
$\sigma^2=(0.2×(19-20.8)²+0.2×(20-20.8)²+0.3×(21-20.8)²+0.2×(22-20.8)²+0.1×(23-20.8)²) / (0.2+0.2+0.3+0.2+0.1) ) = 1.56$
The standard deviation can be found as $\sigma=\sqrt {\sigma^2}=1.249$
If the manager of the retail store wants to be sure that he
has enough suits for the next 5 days, he should purchase
$5\times\mu=5\times20.9=104$ suits.
