Z score and probability Online Calculator
You can see a sample solution below. Enter your data to get the solution for your question
$$ \displaylines{\\ \\ x = 22
\\ \\ \mu = 24.0
\\ \\ \sigma = 2
\\ \\ n = 3
\\\;\\\;Formula\;for\;z\;is
\\ \\ Z=
\frac{x - \mu }{\frac{\sigma }{\sqrt{n}}}
\\ \\ So, Z = \frac{22-24.0}{\frac{2}{\sqrt{3}}}
\\ \\ \Rightarrow
\frac{-2.0}{1.154701}
\\ \\ \Rightarrow
-1.73205
\\ \\ As\;per\;question\;we\;need\;to\;find\;probability\;of\;X<22.\\\;\\\;That\;is\;Z<-1.73205
\\ \\ P(Z<-1.73205)
= \mathbf{\color{Red}{0.041632}} \left [ From\;z\;table \right ]
\\ \\ Therefore\;probability\;of\;x\;less\;than\;22\;is\;\;\mathbf{\color{Red}{0.041632}}
} $$