In an article about unusual allergies, a doctor explained that allergy to sulfites is usually seen in patients with asthma. The typical reaction is a sudden increase in asthma symptoms after eating a food containing sulfites. Studies are performed to estimate the percentage of the nation's 10 million asthmatics who are allergic to sulfites. In one survey, 37 of 500 randomly selected asthmatics in the country were found to be allergic to sulfites. A 95% confidence interval for the proportion, p, of all asthmatics in the country who are allergic to sulfites, was found to be 0.051 to 0.097. Complete parts (a) through (f). Click here to view page 1 of the table of areas under the standard normal curve. Click here to view page 2 of the table of areas under the standard normal curve. a. Determine the margin of error for the estimate of p. The margin of error is (Round to three decimal places as needed.) b. Obtain a sample size that will ensure a margin of error of at most 0.01 for a 95% confidence interval without making a guess for the observed value of p. The sample size would need to be at least] (Round up to the nearest whole number.) c. Find a 95% confidence interval for p if, for a sample of the size determined in part (b), the proportion of asthmatics sampled who are allergic to sulfites is 0.069. The 95% confidence interval of all asthmatics in the country who are allergic to sulfites is from ] to]. (Round to three decimal places as needed.) d. Determine the margin of error for the estimate in part (c) and compare it to the margin of error specified in part (b). The margin of error in part (c) is ], which is the margin of error specified in part (b). Round to three decimal places as needed