Pike Creek Golf Club currently has 375 members who pay annual dues to play golf on the course. Historical records show that 38% of the members use the course at least once a week during the summer season. To verify this, a random sample of 100 members was selected.

a. Calculate the standard error of the proportion.

b. What is the probability that 32 or more members from the sample used the course at least once a week?

c. What is the probability that between 30 and 40 members from the sample used the course at least once a week?

d. If 50 members from the sample used the course at least once a week, does this support the historical records of course usage?