At a baseball stadium, total capacity is 30,000 spectators. Suppose there is a s

Question

At a baseball stadium, total capacity is 30,000 spectators. Suppose there is a sold-out game and all the seats are filled, and that each spectator has a 40% chance of buying one hot dog, a 10% chance of buying two hot dogs, and a 2% chance of buying 3 hot dogs. i) Let X be the number of hot dogs that an individual spectator buys. Determine the mean and variance of X. ii) Let Y be the number of hot dogs that the entire baseball stadium decides to buy. Assuming each spectators actions are independent, determine the mean and variance of Y. iii) Using the central limit theorem, determine the number of hot dogs that the stadium should have ordered so that there is a 99% probability that everyone will be able to buy as many hot dogs as they wish.

Explanation / Answer

(i) from above mean =0.66

and variance =0.5444

(ii) mean of Y =30000*0.66=19800

and variance of Y =0.5444*30000=16332

(iii) std deviation=(16332)1/2 =127.7967

for 99 percentile ; critical z =2.3263

tehrefore corresponding value of hot dogs =mean+Z*std deviaiton =20097.30~ 20098

hot dog x p(x) xP(x) x2P(x) (x-)2 (x-)2P(x) 0 0 0.4800 0.000 0.000 0.436 0.209 1 1 0.4000 0.400 0.400 0.116 0.046 2 2 0.1000 0.200 0.400 1.796 0.180 3 3 0.0200 0.060 0.180 5.476 0.110 total 1 = 0.66 0.980 7.822 2= 0.5444 std deviation=     =    2 = 0.7378

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.