Final answer:
In Mathematics, the mean and variance for the Olympic archer hitting bullseyes with an 80% success rate in 10 shots are 8 and 1.6 respectively.
Step-by-step explanation:
The subject of the question is Mathematics, and it pertains to the calculation of probability and statistics related to repeated independent events, specifically in the context of archery.
Since Kateri Vrakking, an Olympic archer, hits the bullseye 80% of the time and each shot is independent of the others, we can calculate the mean and variance of the number of bullseyes when she shoots 10 arrows.
To find the mean (expected value) of the number of bullseyes, we multiply the probability of hitting a bullseye by the number of shots taken:
Mean = Probability of bullseye × Number of shots = 0.80 × 10 = 8
The variance for a binomial distribution is found using the formula, Variance = n × p × (1 - p), where n is the number of trials and p is the probability of success (hitting the bullseye).
Variance = 10 × 0.80 × (1 - 0.80) = 10 × 0.80 × 0.20 = 1.6
Therefore, the mean number of bullseyes Kateri is expected to hit is 8, and the variance of the number of bullseyes is 1.6.