Attendance at a health club is normally distributed. The average number of peopl

Question

Attendance at a health club is normally distributed. The average number of people visiting the health club at any given time is 100,with a standard deviation of 48.5. The club has a capacity of 200 people.

a. What is the probability the club exceeds capacity?

b. In the past, club workers have wanted to close early on evenings before holidays when attendance was very low. The current club contract with members states that if attendance is below 5 people, the club has the option of closing early. What is the probability the club will close early?

Explanation / Answer

probability people is more than 200=pr(Z>(200-100)/48.5)=pr(Z>2.61)=0.0196

probability people is less than 5=pr(Z<(5-100)/48.5)=pr(Z<-1.95876)=0.02507

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