Question

Owners of a minor league baseball team believe that a Normal model is useful in projecting the number of fans who will attend home games. They use a mean of 8500 fans and a standard deviation of 1500 fans. Using this model, answer these questions. a. Sketch and clearly label this Normal model, based on the 68-95-99.7 Rule. b. What proportion of the home games will have fewer than 6000 fans in attendance? c. What proportion of the home games will have between 9000 and 12000 fans? d. Fill in the blank: Only 5% of the home games will have more than ______________ fans in attendance.

Answer 1

a) Thus, we can say that 68% of times, 7000 to 10,000 fans will attend home games; 95% times 5500 to 11500 fans will attend home games. 99.7% times, 4000 to 13000 fans will attend home games.

Precisely the rule says, 68.27% of times, 7000 to 10,000 fans will attend home games; 95.45% times 5500 to 11500 fans will attend home games. 99.73% times, 4000 to 13000 fans will attend home games.

Let X = Number of fans attending home games; X~N(mean= 8500, sd = 1500)

Let Z~N(0,1) #Standard normal variate

b) Proportion of the home games that will have fewer than 6000 fans in attendance = P(X < 6000) = P(Z < -1.667) = 0.04779

c) proportion of the home games that will have between 9000 and 12000 fans = P(9000 < X < 12000) =

=P(0.333 < Z < 2.33) = 0.3707 - 0.0099 = 0.3608

d) Only 5% of the home games will have more than ______________ fans in attendance.

Thus, P(X>x)=0.05; x = 10967.28

Only 5% of the home games will have more than 10967 fans in attendance.