Business Week reported that business executives want to break down the obstacles that keep them from communicating directly with stock owners. Ms. Borrus reports that 80% of shareholders hold stock in “street names,” which are registered with their bank or brokerage. If the brokerage doesn’t furnish these names to the corporations, executives cannot communicate with their shareholders. To determine if the percent reported by Ms. Borrus is correct, a sample of 20 shareholders was asked if they held their stock in “street names.” Seventeen responded that they did.
a. Supposing the true proportion of shareholders that hold stock under street names is 0.80, calculate the probability that 17 or more of the sampled individuals hold their stock under street names.
b. Repeat the calculation in part a using proportions of 0.70 and 0.90.
c. Based on your calculations in parts a and b, which proportion do you think is most likely true? Support your answer.