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# 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

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