ECO250_Module4_Exercise

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University of North Carolina, Greensboro *

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Economics

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Feb 20, 2024

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ECO250 Module 4 Exercise 1. What is a random variable? Give an example. A random variable has a probability distribution showing the chance of any of the possible values happening. An example is the number of cups that are defective in a box of 30. Suppose you are shopping online for a new toy for your dog. As you look at the product reviews, you see the following distribution of ratings. Use this table for questions 2-5. Stars Frequency 5 9 4 3 3 2 2 1 1 5 2. Sketch a data visualization of the distribution of stars.

3. What is the probability that a randomly chosen reviewer gave the dog toy 3 stars? What is the probability that a randomly chosen reviewer gave the dog toy 3 or fewer stars? Part 1: P(x=3)= 2/20 Part 2: P(3 or fewer stars)=.1+.05+.25 =.1 =.4 4. Find the expected value for the number of stars. =1(.25)+2(0.1)+3(0.1)+4(.15)+5(.45) = 3.5 5. Find the standard deviation of the number of stars. =sqrt 15-(3.5)^2 = sqrt 15-12.25 = sqrt 2.75 =1.658 6. Write down the formula for the binomial distribution. What do n , x , and π represent in the formula? What does n ! mean? Formula is P(x) = n C x · p x (1 − p) n − x n= the number of trials x= the number of successes where x is greater than or equal n = the probability success π n!= the factorial of n

7. As you shop for dog treats, a seller advertises that 95% of veterinarians recommend their treats. Suppose you randomly choose 10 veterinarians and ask whether they recommend this seller’s treats. a. What is the probability that exactly nine veterinarians in your sample recommend the seller’s treats? =10C9(.95)^9(1-0.95)^10-9 =.5(.95)^1 =.315 b. What is the probability that more than eight veterinarians in your sample recommend the seller’s treats? 10C10(.95)^10(1-.95)^10-10 = (.95)^10 =.5(.95)^9+.95)^10 = .914

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