In: Statistics and Probability
According to a study done by Pew Research Center, 210 out of 500 adult Americans believe that marriage is now obsolete.
a. Find the mean and standard deviation of the sampling distribution of ?̂; the sample proportion of adult Americans who believe marriage is obsolete.
b. In a random sample of 500 adult Americans, what is the probability that less than 35% believe marriage is obsolete?
c. What is the probability that in a random sample of 500 adult Americans between 40% and 50% believe marriage is obsolete?
d. Would it be unusual if a random sample of 500 adult Americans resulted in 250 or more who believe marriage is obsolete? (remember that unusual is more than 2 standard deviations from the mean)? Why or why not?