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 147 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Let X = the average of the 49 races.

Part (b) Find the probability that the runner will average between 144 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.)

Part (c) Find the 60th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)

Part (d) Find the median of the average running times.

Explanation / Answer

here as sample size is greater than 30 tehrefore samping distribution of mean should follow normal distribution

b)

  probability that the runner will average between 144 and 148 minutes:

c)

for 60th percentile z score =0.25

therefore corresponding average running time=mean +z*std deviaiton =147.43

d) for median and mean are same for normal distirbution

therefore median of the average running times =147

for normal distribution z score =(X-?)/? here mean=       ?= 147 std deviation   =?= 12.0000 sample size       =n= 49 std error=?x?=?/?n= 1.714

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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