A study of Pennsylvania school wrestlers found that 23% had sustained an injury while wrestling. Suppose a similar study was conducted for South Carolina wrestlers and an estimates of the proportion of injured wrestlers using a 99% level of confidence allowing the error, E, to be within 2.5%. Using the prior study from Pennsylvania, what would be the minimum sample size to use in South Carolina?

a. What is the decimal value for zc?

b. What is the value for p-cap?

c. What is the value for q-cap?

d. To the nearest whole number, what is the minimum sample size for the South Carolina study?