Major League Baseball teams have become concerned about the length of games. Dur

Question

Major League Baseball teams have become concerned about the length of games. During a recent season, games averaged 2 hours and 52 minutes (172 minutes) to com- plete. Assume the length of games follows the normal distribution with a standard deviation of 16 minutes. 6.9 a. What is the probability that a randomly selected game will be completed in 1. 200 minutes or less? 2. more than 200 minutes? 3. 150 minutes or less? 4. more than 150 minutes? 5. exactly 150 minutes? b. What is the completion time in which 90% of the games will be finished?

Explanation / Answer

a) P(X<200)

= P(Z<(200-172)/16)

= 0.9599

b) P(X>200)

= 1-P(X<200)

= 1-0.9599

= 0.0401

c) P(X<150)

= P(Z<(150-172)/16)

= 0.0846

d) P(X>150)

= 1-P(X<150)

= 0.9154

e) P(X = 150)

P(149.5<X<150.5)

= P((149.5-172)/16<Z<(150.5-172)/16)

= 0.0625

b) 90% completion time = 1.645*16+172 = 198.32 minutes

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

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