Answer:
The mean of the distribution is 4.00 and the standard deviation is 2.31
Explanation:
Given
Range = 2 to 10
Type of distribution = uniform distribution
Required
1. Mean
2. Standard Deviation
The mean of uniform distribution is calculated as thus;
[tex]Mean = \frac{1}{2}(a + b)[/tex]
Where b and a are the intervals of the distribution
b = upper bound = 10
a = lower bound = 2
So,
[tex]Mean = \frac{1}{2}(a + b)[/tex]
Substitute 10 for b and 2 for a
[tex]Mean = \frac{1}{2}(2 + 10)[/tex]
[tex]Mean = \frac{1}{2}(12)[/tex]
[tex]Mean = \frac{1}{2} * 12[/tex]
[tex]Mean = 6[/tex]
[tex]Mean = 6.00[/tex] (Approximated to 2 decimal places)
The standard deviation of uniform distribution is calculated as thus;
σ = √σ²
Where σ represents the standard deviation and σ² represents the variance.
Calculate variance
σ² = Var
[tex]Var = \frac{(b-a)^2}{12}[/tex]
Substitute 10 for b and 2 for a
[tex]Var = \frac{(10 - 2)^2}{12}[/tex]
[tex]Var = \frac{8^2}{12}[/tex]
[tex]Var = \frac{64}{12}[/tex]
[tex]Var = 5.33[/tex]
Recall that
σ = √σ² = √Var
Substitute 5.33 for Var
σ = √5.33
σ = 2.309401076758503
σ = 2.31 (Approximated)
Hence, the mean of the distribution is 4.00 and the standard deviation is 2.31