The Placebo Effect A company is testing a new medicine for migraine headaches. In the study, 150 women were given the new medicine and 100 women were given a placebo. Each participant was directed to take the medicine when the first symptoms of a migraine occurred and then to record whether the headache went away within 45 minutes or lingered. The results are recorded in the following table:

(b) If a study participant is selected at random, what is the probability her headache went away within 45 minutes?

"[DATA] A Random Process: Green Lights On your drives to school each day you feel like there is a light that is always red when you reach it. You decide to record data to determine the likelihood of arriving at the light while it is red. Open the data set 5_1_38 at www.pearsonhighered.com/sullivanstats, which contains the day number and whether the light was red (1), or not (0), for 120 consecutive days in which you drove to school.

b. What proportion of the days were you stuck by a red light after 15 days?"

"[DATA] A Random Process: Green Lights On your drives to school each day you feel like there is a light that is always red when you reach it. You decide to record data to determine the likelihood of arriving at the light while it is red. Open the data set 5_1_38 at www.pearsonhighered.com/sullivanstats, which contains the day number and whether the light was red (1), or not (0), for 120 consecutive days in which you drove to school.

f. What is the estimate of the probability of the light being red when you reach the intersection?"

[NW] Medicare Fines In an effort to reduce the number of hospital-acquired conditions (such as infection resulting from the hospital stay), Medicare officials score hospitals on a 10-point scale with a lower score representing a better patient track record. The federal government reduces Medicare payments to those hospitals with the worst scores. The following data represent the scores received by Illinois hospitals.

c. Determine the probability that a randomly selected hospital in Illinois has a score less than 9.

Cigar Smoking The data in the following table show the association between cigar smoking and death from cancer for 139,704 men. Note: Current cigar smoker means cigar smoker at time of death.

b) If an individual is randomly selected from this study, what is the probability that he was a current cigar smoker?

Soccer? In a survey of 500 randomly selected Americans, it was determined that 22 play soccer. What is the probability that a randomly selected American plays soccer?

Apartment Vacancy A real estate agent conducted a survey of 200 landlords and asked how long their apartments remained vacant before a tenant was found. The results of the survey are shown in the table. The data are based on information obtained from the U.S. Census Bureau.

c. Find the probability that a randomly selected apartment is vacant for 1–4 months.

Titanic Survivors The following data represent the survival data for the ill-fated Titanic voyage by gender. The males are adult males and the females are adult females.

a. What is the probability that the passenger survived?

ChatGPT Use According to Pew Research, 26% of U.S. teens ages 13 to 17 using ChatGPT for their schoolwork.

a. What is the probability that four randomly selected 13- to 17-year-olds all use ChatGPT for their schoolwork?