Describing Distribution's Two Properties
Suppose that a company's monthly sales follow a normal distribution. The mean of this distribution is \(\$50000\) and the standard deviation is \(\$5000\). What are the two properties of this distribution?
Finding the Expectation
A fair die is rolled. What is the expected value of the number that shows up?
Finding the Standard Deviation
Given a dataset of {3, 5, 2, 8, 9}, calculate the standard deviation.
Finding the Variance
A die is rolled 60 times. What is the variance of the number of times 3 is rolled?
Finding a z-Score for a Normal Distribution
In a normal distribution, the mean (\(\mu\)) is 12 and the standard deviation (\(\sigma\)) is 2. Find the z-score for x = 15.
Approximating Using Normal Distribution
In a university, the scores of a math final exam are normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that a randomly selected student scored more than 85?
Finding the Probability of a Binomial Distribution
A multiple choice exam has 10 questions. Each question has 4 possible answers, of which only 1 is correct. If a student guesses on each question, what is the probability that the student will get exactly 6 questions correct?
Finding the Probability of the Binomial Event
A multiple choice exam has 10 questions. Each question has four possible answers, of which only one is correct. If a student guesses all the answers, what is the probability that the student will answer exactly 6 questions correctly?
Finding the Mean
Consider a random variable X that follows a binomial distribution with parameters n = 10 and p = 0.5. What is the mean of this distribution?