Data collected over an extended period of time show that women college soccer players have a relatively high rate of concussions, often with life-changing consequences. See Stanford Star Retires and Concussions Derail Promising Careers. For collegiate women soccer players the concussion rate is .63 per 1,000 participation hours (practice and game participation hours), for collegiate men soccer players the concussion rate is .41 per 1,000 participation hours (the concussion rate in college football is .61 per 1,000 participation hours). Use the Poisson distribution to answer the following questions. a. What is the probability that the men's team experiences 2 or more concussions? (Use 3 decimal places).
b. What is the probability that the women's team experiences 2 or more concussions? (Use 3 decimal places).

a) 0.064 = 6.4% probability that the men's team experiences 2 or more concussions

b) 0.131 = 13.1% probability that the women's team experiences 2 or more concussions

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

In this question:

We have to find for both cases.

a. What is the probability that the men's team experiences 2 or more concussions?

For collegiate men soccer players the concussion rate is .41 per 1,000 participation hours. This means that

Either less than 2 get concussed, or at least two do. The sum of the probabilities of these events is decimal 1. So

In which

So

0.064 = 6.4% probability that the men's team experiences 2 or more concussions.

b. What is the probability that the women's team experiences 2 or more concussions?

For collegiate women soccer players the concussion rate is .63 per 1,000 participation hours. This means that

Following the same logic as a.

0.131 = 13.1% probability that the women's team experiences 2 or more concussions

Vertex form: f(x) = -10(x − 2)^2 + 3

Standard form: y = -10x^2 + 40x - 37

Step-by-step explanation:

h and k are the vertex coordinates

Substitute them in the vertex form equation:

f(x) = a(x − 2)^2 + 3

Calculate "a" by replacing "f(x)" with -7 and "x" with 1:

-7 = a(1 − 2)^2 + 3

Simplify:

-7 = a(1 − 2)^2 + 3

-7 = a(-1)^2 + 3

-7 = a + 3

-10 = a

Replace a to get the final vertex form equation:

f(x) = -10(x − 2)^2 + 3

Convert to standard form:

y = -10(x − 2)^2 + 3

Expand using binomial theorem:

y = -10(x^2 − 4x + 4) + 3

Simplify:

y = -10x^2 + 40x - 40 + 3

y = -10x^2 + 40x - 37