1. Sample and Population Proportions. In the latest data available, there were 22,782 physicians in Ohio, of whom 2,444 were surgeons. One particular hospital has 14 physicians of whom 2 are surgeons.

a. What is the proportion of surgeons in the state population of physicians (round to two decimal places)?

b. What is the proportion of surgeons in the hospital physician sample (rounded to two decimal places)?

c. Based on the population proportion and the sample size, what is the standard deviation of the sampling distribution of all possible samples of the same size drawn from this population? Round the final answer to 3 decimal places.

d. Using the appropriate version of the z formula, how many standard deviation units is the sample proportion away from the mean of the distribution of sample proportions? round the final answer to 2 decimal places.

e. Based on the z you just calculated what is the probability of selecting a sample with the proportion you calculated in part b or less from this sampling distribution.