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Answer :
Final answer:
The variance of the number of days Pete will catch fish when he goes fishing three days next week is 0.48.
Explanation:
To calculate the variance, we can use the formula for the variance of a binomial distribution, which is Var(X) = np(1-p), where n is the number of trials and p is the probability of success on each trial. In this case, Pete is going fishing three days (n = 3) next week, and the probability of him catching fish on any given day is 0.8 (p = 0.8).
Var(X) = 3 * 0.8 * (1 - 0.8) = 3 * 0.8 * 0.2 = 0.48
So, the variance of the number of days Pete will catch fish is 0.48. This means that when Pete goes fishing three days next week, on average, he can expect to catch fish on 2.4 days (3 * 0.8), and the variance tells us how much the actual number of days may vary around this average.
In this case, a variance of 0.48 implies that there is some variability in Pete's fishing success, but it's relatively low.
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Final Answer:
The variance of the number of days Pete will catch fish is 0.48.
Explanation:
The variance of a binomial distribution can be calculated using the formula: Variance = n * p * (1 - p), where n is the number of trials and p is the probability of success.
In this case, Pete is going fishing for 3 days (n = 3) and the probability of him catching fish on any given day is 0.8 (p = 0.8). Plugging these values into the formula, we get:
Variance = 3 * 0.8 * (1 - 0.8) = 3 * 0.8 * 0.2 = 0.48.
So, the variance of the number of days Pete will catch fish is 0.48. This means that, on average, Pete is expected to catch fish on 3 * 0.8 = 2.4 days, and the variance represents the degree of variability or spread around this average.
Variance in probability and statistics helps measure how data points differ from the mean or expected value. It's a useful concept to understand the degree of uncertainty or variability in a given situation.
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