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In: Statistics and Probability

A large company (with over 10,000 employees) gives end-of-year bonuses out to their employees for excellent...

A large company (with over 10,000 employees) gives end-of-year bonuses out to their employees for excellent performance. They decide to give exactly 30% of their employees a bonus.

a) You share your office with three other employees (four of you in total). What is the probability that at least one of you gets a bonus if bonuses were handed out randomly? b) The data science team consists of 50 employees and receives 25 bonuses. What is the probability of a randomly selected group of 50 employees receives 25 or more bonuses?

c)Interpret the result in part (b).

d) Bonus pay is distributed with a mean of $5,000 and a standard deviation of $2,000. If you receive a bonus, what is the probability your bonus is greater than $6,000?

e) What is the probability that the average bonus pay for the data science team is greater than $6,000?

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