Question

(1 point) In a recent collegiate men's 5000 meter speed skating competition, the average time was 411 seconds and the SD was 11.1 seconds. Assume that the times follow the normal curve and round all calculated results to four decimal places. 1. Find the percentage of skaters who would take longer than 434 seconds to finish the race. % 2. Using the normal curve, find a skater's time if he has a percentile rank of 69 (i.e. 31% of the skaters take longer than him to finish the race). In seconds

Answer 1

Solution :

Given ,

mean = = 411

standard deviation = = 11.1

P(x >434 ) = 1 - P(x<434 )

= 1 - P[(x -) / < (434 -411) / 11.1]

= 1 - P(z <2.07 )

Using z table

= 1 - 0.9808

= 0.0192

answer=1.9%

(b)

Using standard normal table,

P(Z < z) = 69%

=(Z < z) = 0.69  

= P(Z <0.50 ) = 0.69

z = 0.50

Using z-score formula  

x = z +

x = 0.50*11.1+411

x = 416.55

x=417