# Average 10.Variance 25.00. sample of 30 students. Find the probability that I). less than 8.00 ? II).between 8.00 and 13.00 ?

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#### Explanation:

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Feb 7, 2018

$\text{I) P = 0.3085}$
$\text{II) P = 0.4495}$

#### Explanation:

$\text{variance = 25" => "standard deviation } = \sqrt{25} = 5$
$\text{We go from N(10, 5) to normalized normal distribution :}$
I)
$z = \frac{7.5 - 10}{5} = - 0.5$
$\implies P = 0.3085 \text{ (table for z-values)}$
II)
$z = \frac{13.5 - 10}{5} = 0.7$
$\implies P = 0.7580 \text{ (table for z-values)}$
$\implies P \left(\text{between 8 and 13}\right) = 0.7580 - 0.3085 = 0.4495$

$\text{7.5 and 13.5 instead of 8 and 13 because of a continuity}$
$\text{correction to the discrete values.}$

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