Statistics Review Sampling, Binomial, ANOVA 1. a) Arandom sample of size 25 is selected from a normally distributed population with a mean of 16 and a standard deviation of 4. What is the probability that the sample mean is somewhere between 15.8 and 16.2? b). A normally distributed population has a mean of 16 and a standard deviation of 4. What is the probability that a single event is somewhere between 15.8 and 16.2? 2. Suppose that the miles-per-gallon rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 and 3.5 mpg, respectively. a) What is the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg? b What is the probability that the average mpg of four randomly selected passenger cars is between 35 and 38 mpg? c) What is the probability that the average mpg off four randomly selected passenger cars is less than 38 mpg? 3. A marketing firm finds that 16% of advertising contacts result in a purchase. Five customers are randomly selected and are emailed an advertisement. a) What is the probability that no more than one customer makes a purchase? Use Binomial formula. b) What is the E(X)? 4. A recent study revealed that 75% of business travelers make their own travel arrangements. The study is to be replicated with a sample of 10 frequent business travelers. Use Binomial table. a. What is the probability exactly 4 travelers make their own travel arrangements? b. What is the probability 9 or more travelers make their own travel arrangements? c. Calculate the expected value AND the standard deviation. 5. ltis estimated that about 35% of California residents have adequate earthquake supplies. You randomly survey 10 California residents. Use Binomial table. a. What is the probability that at least eight have adequate earthquake supplies? b. What is the probability that less than three have adequate earthquake supplies? c. How many residents do you expect will have adequate earthquake supplies? What is standard deviation? 6. In a restaurant, the proportion of people who order coffee with their dinner is 0.9. A simple random sample of 144 patrons of the restaurant is taken. a) What is the probability that the proportion of people who will order coffee with their meal is between 0.85 and 0.8757 b) What is the probability that the proportion of people who will order coffee with their meal is at least 0.945? 7. A researcher wants to find the relationships between the dependent variable and 4 independent variables. Complete the ANOVA table with 22 observations: df SS MS F | Regression 120.66 | Residual Total 150.84 = 8. When you sketch the middle 85%, the distribution has two tails, an upper tail, and a lower tail. What is the percentage of each tail? What are the Z values? 357 When you sketch with only one tail of 15%, what is the Z value