Mathematics: How do you write 8.65 x 10^4 in standard form?

How do you write 8.65 x 10^4 in standard form? - id8651048364181, asdfghj3513

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28.12.2021

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%

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