Question
3.) A street performer gathers an audience and picks a random person to stand in a designated space. He then jumps completely over that person.
3.) A street performer gathers an audience and picks a random person to stand in a designated space. He then jumps completely over that person. He can clear any person who is 76.1 inches tall or less. If a person is taller than that, he will make contact with them in his jump, fail his trick, and risk injury to them and himself. This is incredibly rare.
The performer is considering moving to a new street. However, he is concerned that there are more men on this street and so it is more likely that his randomly chosen audience member will be taller. After scouting, he determined that 62% of the people in his audience would be male. He has determined that the height of males on the street is normally distributed with a mean of 71 inches and a standard deviation of 3 inches. He has determined that the height of females on the street is normally distributed with a mean of 69 inches and a standard deviation of 3.9 inches.
i.) If Jon picks a member of his audience completely at random, what is the probability that he will fail on his trick (i.e., fail to fully clear them on his jump)?
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