On a certain standardized test used for college entrance purposes, the mean score was 21 and the standard deviation was 5. The distribution was approximately normal. Carlos scored 31, two standard deviations above the mean. A total of 1.5 million people across the country took the test at the same time as Carlos. How many people had scores lower than Carlos?

a. 1,465,500 people
b. 977,000 people
c. 204,000 people

The vice president of programming at nbc is finalizing the prime-time schedule for the fall. she has decided to include a hospital drama but is unsure which of two possibilities to select. she has a pilot called the surgeon and another called critical care. to her make a final decision, a sample of 20 viewers from throughout the united states was asked to watch the two pilots and indicate which show they prefer. the results were that 12 liked the surgeon, 7 liked critical care, and one had no preference. state the decision rule, using the 0.10 significance level. h0: π = 0.50 h1: π ≠ 0.50 1. reject h0 if number of + signs is either < = or > = 2. what is your decision regarding h0? is there a preference for one of the two shows?