1. Problem number 35 part a-c page 138 of Textbook. Pike Creek Golf Club current

Question

1. Problem number 35 part a-c page 138 of Textbook. Pike Creek Golf Club currently has 375 members who pay annual dues to play on the course. Historical records show that 38% of the members use the course at least once a week during the summer. To verify this, a random sample of 100 members were selected. A. Calculate the standard error of proportion B. What will be 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 S0 members from the sample used the course alt records of coue usoes this suport the historical

Explanation / Answer

p = 0.38
n = 100

A.
Standard Error = sqrt(p*(1-p)/n) = sqrt(0.38*0.62/100) = 0.0485

B.
mean = 100*0.38 = 38
std. dev. = sqrt(p*(1-p)*n) = sqrt(0.38*0.62*100) = 4.8538

P(X > 32)
= P(z > (32 - 38)/4.8538)
= P(z > -1.2361)
= 0.8918 (value found using standard z-table)

C.
P(30 < X < 40)
= P((30 - 38)/4.8538 < z < (40 - 38)/4.8538)
= P(-1.6482 < z 0.4120)
= P(z < 0.4120) - P(z < -1.6482)
= 0.6598 - 0.0496 (values found using standard z-table)
= 0.6102

D. Yes this supports the historical records of course usage as n > 30.

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