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 14 minutes. Consider 49 of the races. Let X = the average of the 49 races. Part (a) Give the distribution of X. X = () Part (b) Find the probability that the runner will average between 143 and 146 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 80 the percentile for the average of these 40 marathons. min Part (d) Find the median of the average running times. min

Explanation / Answer

here mean of Xbar =145

and std deviation =14/(49)1/2 =2

hence Xbar =N(145 ,2 ) please revert as some time they take variance for parameter and we have to put 4 in place of 2)

b)P(143<X<146) =P(-1<Z<0.5)=0.6915-0.1587=0.5328 for ti-84 =normalcdf(143;146,145,2) will give u result

c) for 80th percentile z=0.8416

hence coprresponding value =mean +z*std deviation =145+0.8416*2 =146.68

from ti-84 ; =invnorm(0.8 ;145,2)

d) for normal distribution median =mean =145

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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