Z score and probability between two values Calculator
You can see a sample solution below. Enter your data to get the solution for your question
$$ \displaylines{---} $$
$$ \displaylines{x1 = 4
\\ \\
x2 = 9
\\ \\
\mu = 6
\\ \\ \sigma = 2.5
\\ \\ n = 15
\\ \\
\mathbf{\color{Green}{First\;we\;have\;to\;find\;z\;value\;for\;x_{1}}}
\\ \\
Formula\;for\;z\;is
\\ \\ Z=
\frac{x - \mu }{\frac{\sigma }{\sqrt{n}}}
\\ \\ So, Z = \frac{4-6}{\frac{2.5}{\sqrt{15}}}
\\ \\ \Rightarrow
\frac{-2}{0.645497}
\\ \\ \Rightarrow
-3.098388
\\ \\
\mathbf{\color{Green}{Now\;we\;have\;to\;find\;z\;value\;for\;x_{2}}}
\\ \\
Formula\;for\;z\;is
\\ \\ Z=
\frac{x - \mu }{\frac{\sigma }{\sqrt{n}}}
\\ \\ So, Z = \frac{9-6}{\frac{2.5}{\sqrt{15}}}
\\ \\ \Rightarrow
\frac{3}{0.645497}
\\ \\ \Rightarrow
4.647582
\\ \\ As\;per\;question\;we\;need\;to\;find\;probability\;of\;4<X<9.\\\;\\\;That\;is-3.098388<Z<4.647582
\\ \\ P(-3.098388<Z<4.647582)
= \mathbf{\color{Red}{0.999025}} \left [ From\;z\;table \right ]
\\ \\ Therefore\;probability\;of\;x\;between\;4\;and\;9\;is\;\;\mathbf{\color{Red}{0.999025}}
} $$