4) An association football (soccer) striker never hits the ball above the crossbar. However, in the...

4) An association football (soccer) striker never hits the ball above the crossbar. However, in the horizontal direction, his strikes are normally distributed and centered 3 feet to the left of the goal center with a standard deviation of 8 feet. What is the probability that he will score a goal on a given attempt? (Hint: You need to first find the width of a soccer goal. Also, assume that all strikes in the goal region result in a goal.)

Solutions

Expert Solution

Let X be the distance from the goal center (in the horizontal direction) that the striker strikes on any given attempt, such that X is positive if it is to the right of the goal center and is negative if it is to the left of the goal center. We can say that X has a normal distribution with mean (it is towards the left of goal center) and standard deviation

The width of a soccer goal is 24 feet. The striker will score if he strikes within 12 feet from the goal center.

the probability that he will score a goal on a given attempt is

ans: the probability that he will score a goal on a given attempt is 0.8407

orchestra answered 1 year ago

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