Discuss the below:
1. A study by the National Park Service revealed that 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.
a. What is the probability a vacationer will visit at least one of these attractions?
b. What is the probability .35 called?
c. Are the events mutually exclusive? Explain.
2. In a binomial situation n _ 5 and _ _ .40. Determine the probabilities of the following
events using the binomial formula.
a. x _ 1
b. x _ 2
3. A normal population has a mean of 80.0 and a standard deviation of 14.0.
a. Compute the probability of a value between 75.0 and 90.0.
b. Compute the probability of a value 75.0 or less.
c. Compute the probability of a value between 55.0 and 70.0.
4. The mean rent for a one-bedroom apartment in Southern California is $2,200 per month. The distribution of the money costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one- bedroom apartments and finding the mean to be at least $1,950 per month? The standard deviation of the sample is $250.
5. Dr. Patton is a Professor of English. Recently he counted the number of misspelled words in a group of student essays. For his class of 40 students, the mean number of misspelled words was 6.05 and the standard deviation 2.44 per essay. Construct a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.