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Answer: Variance = 0.858
Step-by-step explanation: The variance formulae for a probability distribution is given below as
Variance = √npq
Where n = number of times experiment was performed = 9
p = probability of success = 0.09
q = probability of failure = 1 - p = 1 - 0.09 =0.91
Variance = √9×0.09×0.91
Variance = √0.7371
Variance = 0.858
The variance of the number of bull's-eyes scored is 0.737
Since, An archer hits a bull’s-eye with a probability of 0.09
So, probability of success is, [tex]p=0.09[/tex]
Probability of unsuccessful, [tex]q=1-p[/tex]
[tex]1-0.09=0.91[/tex]
Number of trial, [tex]n=9[/tex]
In binomial distribution,
Variance = [tex]n*p*q[/tex]
substituting the value of n, p and q in above expression.
Variance = [tex]9*0.09*0.91=0.737[/tex]
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