Answer:
1.96
Step-by-step explanation:
Solution:-
- We will use the table given to determine the standard deviation of random variable x. From descriptive statistics we have the following formula for standard deviation (s.d) :
s.d (x) = sqrt ( Var(x) )
- The formula for Variance ( Var (x) ) is also taken from descriptive statistics as follows:
[tex]Var(X) = E ( X^2) + [ E(X) ] ^2[/tex]
- Where,
[tex]E ( X^2) = 0^2*0.15 + 1^2*0.07 + 2^2*0.19 + 3^2*0.09 + 4^2*0.16 + 5^2*0.23 +6^2*0.11 \\\\E ( X^2) = 13.91 \\\\[/tex]
[tex]E(X) = 0*0.15\:+\:1*0.07\:+\:2*0.19\:+\:3\cdot \:0.09\:+\:4\cdot \:0.16\:+\:5\cdot \:0.23\:+6\cdot \:0.11\\\\E(X) = 3.17\\\\(E(X))^2 = 10.0489[/tex]
- So the variance is:
Var ( X ) = 13.91 - 10.0489 = 3.8611
s.d (x) = √3.8611 = 1.96
