Question

find the area of the shaded region. 106 and 126
with a mean of 100 and standard deviation of 15

Answer 1

$\textup{Lower Limit, }X_{L}=106\textup{ and Upper Limit, }X_{U}=126$

$\textup{z--scores are defined as, }z=\frac{X-\mu }{\sigma }.\textup{ Given, }\mu =100\textup{ and }\sigma =15$

$\textup{Hence, }z_{L}=\frac{106-100}{15}=0.4\textup{ and }z_{U}=\frac{126-100}{15}=1.7333$

$\textup{Required area}=\mathbb{P}(Z\leq 1.7333)-\mathbb{P}(Z\leq 0.4)$

$\approx 0.9585-0.6554=0.3031$