Question 2

The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medicare service. For this group, 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012). Suppose 10 first-round appeals have just been received by a Medicare appeals office.

1. Compute the probability that none of the appeals will be successful.
2. Compute the probability that exactly one of the appeals will be successful.
3. What is the probability that at least two of the appeals will be successful?
4. What is the probability that more than half of the appeals will be successful?

Question 3

The average price for a gallon of gasoline in the United States is $3.73 and in Russia, it is $3.40 (Bloomberg Businessweek, March 5-March 11, 2012). Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $.25 in the United States and a standard deviation of $.20 in Russia.

1. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon?
2. What percentage of the gas stations in Russia charge less than $3.50 per gallon?
3. What is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States?

Question 4

The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend would spend an average of $749 (The Associated Press, August 12, 2012). Assume that the amount spent is normally distributed with a standard deviation of $225.

1. What is the probability of family expenses for the weekend being less that $400?
2. What is the probability of family expenses for the weekend being $800 or more?
3. What is the probability that family expenses for the weekend will be between $500 and $1000?
4. What would the Labor Day weekend expenses have to be for the 5% of the families with the most expensive travel plans?

Question 5

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55.

1. What is the probability that a hotel room costs $225 or more per night?
2. What is the probability that a hotel room costs less than $140 per night?
3. What is the probability that a hotel room costs between $200 and $300 per night?
4. What is the cost of the 20% most expensive hotel rooms in New York City?