Discuss the below:
1. If a gambler rolls two dice and gets a sum of 10. he wins $10, and if he gets a sum of three, he wins$20. The cost to play is $5. What is the expectation of this game?
2. A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person will die before the age of 65?
3. At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years. If an employee is picked at random, what is the probability that the employee has worked at the store for over 10 years?
4. The average age of a vehicle registered in the United States is 8 years, or 96 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 98 and 100 months? Assume the standard deviation for the population is 15.
5. What is the z value such that 50% of the total area lies to the right of the curve in a normal distribution?
6. A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?
7. The standard deviation of a distribution is 20. If a sample of 225 is selected, what is the standard error of the mean?