Sullivan Survey: Car Color According to paint manufacturer DuPont, 6% of all cars worldwide are red. In the Sullivan Statistics Survey, of 175 respondents, 17, or 9.7%, indicated the color of their car is red. Determine if the results of the Sullivan Survey contradict those of DuPont by computing P(X ≥ 17), where X is a binomial random variable with n = 175 and p = 0.06. Explain what the probability represents.
Step 1 of 5) Sullivan Survey: Car Color According to paint manufacturer DuPont, 6% of all cars worldwide are red. In the Sullivan Statistics Survey, of 175 respondents, 17, or 9.7%, indicated the color of their car is red. Determine if the results of the Sullivan Survey contradict those of DuPont by computing P(X ≥ 17), where X is a binomial random variable with n = 175 and p = 0.06. Explain what the probability represents. Consider a filling machine (such as a coffee machine) that over- and underfills cups, but, on average, fills correctly. Customers are not happy about underfilled cups, and they are dissatisfied with overfilled cups because of spilling. They want a machine that consistently delivers the correct amount. As another example, consider a mutual fund that invests in the stock market. An investor would prefer consistent year-to-year returns near 12%, rather than returns that fluctuate wildly, yet result in a mean return of 12%. Both of these situations illustrate the importance of measuring variability. The main idea is that the standard deviation and the variance are measures of consistency. The less consistent the values of a variable are, the higher the standard deviation of the variable. We begin by reviewing the chi-square distribution.
