Question

The annual precipitation data of a city is normally distributed with mean and standard deviation a 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

• A. <50%
• B. 50%
• C. 75%
• D. 100%

Answer 1

The correct option is A <50%

$\mu =1000,\sigma =200,z=\frac{x-\mu }{\sigma }$
& x = {Annual precipitation data}

$z=\frac{1200-1000}{200}=1$


Required Probability is
P(x > 1200)
= P(Z > 1) $=0.5-P(0<Z<1)$
$<0.5$