Suppose that a category of world class runners are known to run a marathon (26 m

Question

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 15 minutes. Consider 49 of the races. Let bar X the average of the 49 races. (a) Give the distribution of bar X. (Round your standard deviation to two decimal places.) bar X = (b) Find the probability that the runner will average between 143 and 146 minutes in these 49 marathons. (c) Find the 60th percentile for the average of these 49 marathons. (d) Find the median of the average running times. min

Explanation / Answer

Part B

the probability that the runner will average between 143 and 146 minutes in these 49 marathons.

P(143 < X < 146)

= P( ( 143 - 145)/(15/49)) < Z < (146 - 145)/(15/49))

= P( -0.93 < Z < 0.46)

=P( Z < 0.46) - P( Z < -0.93)

= 0.6772 - 0.1761

= 0.5011

Part C

P( X < x) = 0.60

P( Z < (x - 145)/15/49) = 0.60

(x - 145)/15/49 = 0.641

x = 145.091

Part D

the median of the average running times.is 145

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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