!.The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. Find the mean, variance, and standard deviation.

Number of accidents/probability- 0/0.4 1/0.2 2/0.2 3/0.1 4/0.1

2.Dice Game- A person pays $2 to play a certain game by rolling a single die once. If a 1 or a 2 comes up, the person wins nothing. If, however, the player rolls a 3,4,5, or 6, he or she wins the difference between the number rolled and $2. Find the expectation if a person buys one ticket.

3.A student takes a 20-question, multiple-choice exam with five choices for each question and guesses on each question. Find the probability of guessing at least 15 out of the 20 correctly. Would you consider this event likely or unlikely to occur? Explain your answer.

4. It has been reported that 83% of federal government employees use email. If a sample of 200 federal government employees is selected, find the mean, variance, and standard deviation of the number who use email.

5.In recent years, 13% of business have eliminated jobs. If 5 businesses are selected at random, find the probability that at least 3 have eliminated jobs during tat year.