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Answer :
Final answer:
The random variable X refers to how many days Pete catches fish in a week. Given Pete fishes for 3 days with a success probability of .8, using the binomial variance formula, we find the variance to be .48.
Explanation:
To find the variance of the number of days Pete will catch fish (random variable x), you can use the binomial distribution since there are a fixed number of trials (3 days) and a constant probability of success (0.8).
The variance of a binomial distribution can be calculated using the formula:
Variance (σ²) = n x p x (1 - p)
Where:
n is the number of trials (3 days in this case).
p is the probability of success (Pete catching fish on a given day, which is 0.8).
Plug in the values:
Variance (σ²) = 3 x 0.8 x (1 - 0.8)
Variance (σ²) = 3 x 0.8 x 0.2
Variance (σ²) = 0.48
So, the variance of the number of days Pete will catch fish is 0.48.
Learn more about Probability and Variance here:
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