(8 points) A nationwide survey of working adults indicates that only 50% of them are satisfied with their jobs. The president of a large company believes that more than 50% of employees at his company are satisfied with their jobs. To test his belief, he surveys a random sample of 100 employees, and 54 of them report that they are satisfied with their jobs. Can he conclude that more than 50% of employees at the company are satisfied with their jobs? Use the α = 0.05 level of significance. State: Write the null and alternative hypotheses and label all given values with appropriate notation. Plan: 1. Is it a simple random sample? 2. Is our population size large enough so that our sample is independent? 3. Can we use a normal distribution with our sample? Do: Find z-score and P-value using a calculator or chart. What is the result? Conclude: Interpret your result in the context of the problem

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?