Maggie is practicing her penalty kicks for her upcoming soccer game. During the practice, she attempts 10 penalty kicks. If each attempt at the penalty kick is independent of the other attempts and if she scores 65% of the time, historically, what is the probability that she scores at least eight goals? Give your answer as a percentage precise to two decimal places.

26.17%

Step-by-step explanation:

Probability she scored at least 8 goals = probability that she scores 8 goals + probability that she scores 9 goals + probability that she scores 10goals.

Probability of each goal is approximated by the probability distribution formula for selection. From a larger n sample, with a varied sample r, probability is denoted by:

P(X=r) = nCr × p^r × q^n-r

Where p = probability of success = 65% = 0.65

q = 1-p = 1 - 0.65 = 0.35

n = 10

r is varied between 8, 9 and 10.

When r = 8

P(X=8) = 10C8 × 0.65^8 × 0.35² = 0.1757

When r = 9

P(X=9) = 10C9 × 0.65^9 × 0.35¹ = 0.0725

When r = 10

P(X=10) = 10C10 × 0.65^10 × 0.35^0 = 0.0135

Summation of all probabilities = 0.1757 + 0.0725 + 0.0135 = 0.2617

Probability of scoring at least 8goals = 0.2617 = 26.17%

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