According to an expert for the automotive industry, 55% of Americans know how to drive a manual transmission vehicle.
Suppose 380 Americans are sampled. (Give results accurate to at least 4 decimal places.)
a. Of the 380 people sampled, 222 respond that they know how to drive a manual transmission vehicle. What is the sample statistic $\hat{p}$?
$\hat{p}=$
b. Under the assumption that the industry expert's claim that 55% of Americans know how to drive a manual transmission vehicle is valid, what is the probability that the survey in part (a) would result in a $\hat{p}$ that is at least as high as the one found?
c. Under the assumption that the industry expert's claim that 55% of Americans know how to drive a manual transmission vehicle is valid, what is the probability that the survey in part (a) would result in a $\hat{p}$ that is between 53% and 56%?