The standard deviation of the distribution is 1.62
A probability distribution shows how individual probabilities are distributed
The table entries are given as:
wins 1 2 3 4 5 6 7
drivers 12 2 0 2 0 0 1
Calculate the total number of drivers
[tex]Total = 12 +2+0+2+0+0+1[/tex]
[tex]Total = 17[/tex]
Divide the number of drivers by the total, to determine the probability distribution
The probability distribution is as follows:
Wins Drivers P(x)
1 12 0.71
2 2 0.12
3 0 0
4 2 0.12
5 0 0
6 0 0
7 1 0.06
We start by calculating the variance using:
[tex]V(x) = E(x^2) - E(x)^2[/tex]
Where:
[tex]E(x) = \sum x \times P(x)[/tex]
So, we have:
[tex]E(x) = 1 \times 0.71 + 2 \times 0.12 + 3 \times 0 +4 \times 0.12 + 5 \times 0 + 6 \times 0 + 7 \times 0.06[/tex]
[tex]E(x) = 1.85[/tex]
[tex]E(x^2) = 1^2 \times 0.71 + 2^2 \times 0.12 + 3^2 \times 0 +4^2 \times 0.12 + 5^2 \times 0 + 6^2 \times 0 + 7^2 \times 0.06[/tex]
[tex]E(x^2) = 6.05[/tex]
The equation becomes
[tex]V(x) = E(x^2) - E(x)^2[/tex]
[tex]V(x) = 6.05 - 1.85^2[/tex]
[tex]V(x) = 2.63[/tex]
Take the square root of the variance, to calculate the standard deviation.
[tex]\sigma = \sqrt{2.63[/tex]
[tex]\sigma = 1.62[/tex]
Hence, the standard deviation is 1.62
Read more about probability distribution at:
https://brainly.com/question/15246027
