Answer: 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%
