Pike Creek Golf Club currently has 375 members that pay annu

Pike Creek Golf Club currently has 375 members that pay annual dues to play gold 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 1000 members was selected.

a.) Calculate the standard error of the proportion.

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

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

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

Solution

Given P=0.38; Q=1-0.38 = 0.62; n =1000

Standard error of proportion = Sqrt( P*Q/n)=sqrt(0.000236) = 0.015349

b) Mean = nP =1000*0.38 = 380; Varaince = n*P*Q=380*0.62 = 235.6; SD =15.35

P(x>32) = P[z>(32-380)/15.35] =P(z>-22.671) =1

c) P(30<X<40) = P[(30-380)/15.35<z<(40-380)/15.35] = 0

d) No, there is signficant difference between the actual (50) the average number of members (380) in the sample used the course at least once a week