Stats Practice Question

Question

World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 15 minutes.

If we sampled a group of world class runners from a particular race, find the probability of the following:

**(use 4 decimal places)**

a.) The probability that one runner chosen at random finishes the race in less than 140 minutes. 

b.) The probability that 10 runners chosen at random have an average finish time of less than 140 minutes. 

c.) The probability that 50 runners chosen at random have an average finish time of less than 140 minutes. 

Answer 1

a) p (X<140)

On a TI-84.

2nd VARS. normalcdf. lower = -1E99 upper = 140 mean = 146 standard deviation = 15

b) mean will have normal distribution with mean = 146, standard deviation 15/√10

p (mean < 140),

2nd VARS normalcdf, lower = -1E99, mean = 146, standard deviation = 15/√10

c)Same idea as (b) just change the 10 to 50