Question

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 75% 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.

Answer 1

Answer:

The Probability that she scores at least 8 goals is 52.56%

Step-by-step explanation:

Consider the provided information.

She scores 75% of the time (p) = 0.75

q = 1-p = 1-0.75 = 0.25

She attempts 10 penalty kicks.

Thus, n = 10 , p = 0.75 and q = 0.25

According to the binomial distribution.

$P(X) = ^nC_x p^x q^{n-x}$

We need to calculate the probability that she scores at least eight goals.

This can be written as:$P(X \geq 8)$

$P( X\geq 8) = P( X = 8) + P( X = 9) + P( X = 10)$

$p(X\geq 8)= ^{10}C_8 (0.75)^8(0.25)^2 +^{10}C_9 (0.75)^9 (0.25)+^{10}C_{10} (0.75)^{10}0.25^0$

$p(X\geq 8)=\frac{10!}{8!2!}(0.75)^8(0.25)^2 +\frac{10!}{9!1!}(0.75)^9 (0.25)+(0.75)^{10}0.25^0$

$p(X\geq 8)=45(0.75)^8(0.25)^2 +10(0.75)^9 (0.25)+(0.75)^{10}$

$p(X\geq 8)\approx0.5256=52.56\%$

Hence, the Probability that she scores at least 8 goals is 52.56%