Question

Answer the next two questions based on the following information. Winning times in 26 mile marathons run by world-class runners average 145 minutes with a standard deviation of 14 minutes. A sample of the last ten marathon winning times is collected. Let X be the mean winning times for ten marathons.

What is the probability that the mean waiting times for ten marathons is at least 145 minutes?

		0.1
		0.2
		0.3
		0.4
		0.5

Answer 1

Solution :

Given that ,

mean = = 145

standard deviation = = 14

n = 10

= 145

= / n = 14/ 10 = 4.4272

P( >145 ) = 1 - P( <145 )

= 1 - P[( - ) / < (145-145) /4.4272 ]

= 1 - P(z <0 )

Using z table

= 1 -0.5

= 0.5

probability= 0.5