The next two questions refer to the table given below, which breaks down 100 people based upon their gender and age.

One person is randomly selected from this group of 100 people.

Male Female Total

Young 18 27 45

Middle Aged 18 17 35

Senior 4 16 20

Total 40 60 100

One person is randomly selected from this group of 100 people.

1. What is the probability that the person selected is Young or a Female?

2. If a Female is selected, what is the probability that she is Young?

3. The first AUM baseball player coming to bat in an inning gets a hit 25% of the time. The second player coming to bat in an inning gets a hit 32% of the time. Consider their at-bats together, assuming that the outcomes of these two at-bats are independent of each other. What is the probability that neither of them gets a hit?

4. Three horses are running a race. Their names are Xeron (X), Yellowfly (Y), and Zonks (Z). They are equally likely to win the race.

(a) List all the possible orders in which these horses could finish the race.

(b) MIke bets that the horses will finish in the order YXZ. What is the probability that at least one of the horses will finish in the position that he predicts?

5. Regal Cinemas commissioned a national study to determine the amount of money spent on concessions by their customers. The study revealed that the amount spent follows a normal distribution with a mean of $6.11 and a standard deviation of $1.87.

(a) What proportion of all customers of Regal Cinemas spend more than $10.00 on concessions?

(b) What percentage of all customers of Regal Cinemas spend between $5.00 and $10.00 on concessions on a typical outing at the movies?

(c ) Determine the 90th percentile for money spent on concessions by Regal Cinemas customers.

6. An IRS agent must review a stack of 9 randomly chosen tax returns for mistakes. If mistakes occur in 10% of the returns, what is the probability that there is at most four returns with a mistake?(Binomial distribution)

7. If electricity power failures occur according to a Poisson distribution with an average of three failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week.

8. Suppose that you have a bag filled with 50 marbles, 15 of which are green. What is the probability of choosing exactly 3 green marbles if a total of 10 marbles are selected? (Hypergeometric distribution)

9. Calls arrive at an average rate of 12 per hour. Find the probability that a call will occur in the next 5 minutes given that you have already waited 10 minutes for a call> (Exponential Distribution)

10. Body temperature have an average of 98.6 and a standard deviation of 0.62. A sample of 106 people were selected. What is the probability that the average temperature for the sample will be 98.2 or lower?