The president of Doerman Distributors, Inc., believes that 31% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers. Use z-table.

a. What is the probability that the sample proportion will be between 0.22 and 0.40 (to 4 decimals)?

b. What is the probability that the sample proportion will be between 0.27 and 0.35 (to 4 decimals)?