Question

To qualify for a particular race, runners must complete a qualifier. Generally, runners who enter the qualifier have a mean time of 35 minutes with a standard deviation of 2 minutes. A runner automatically qualifies if their time is less than 30 minutes. What proportion of runners complete the race in between 34 and 37 minutes?

Answer 1

Solution :

Given that,

mean = = 35

standard deviation = = 2

a ) P( x < 30 )

P ( x - / ) < ( 30 - 35 / 2)

P ( z < - 3 / 2 )

P ( z < -1.5 )

= 0.0668

Proportion = 0.0668

b ) P (34 < x < 331 )

P ( 34 - 35 / 2) < ( x -  / ) < ( 37 - 35 / 2)

P ( - 1 / 2 < z < 2 / 2 )

P (-0.5 < z < 1 )

P ( z < 1) - P ( z < -0.5)

Using z table

= 0.8413 - 0.3085

= 0.5328

Proportion= 0.5328