Question

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 149 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.

  (Round your standard deviation to two decimal places.)

  X

  ~     ,  

• Part (b)

  Find the probability that the average of the sample will be between 148 and 151 minutes in these 49 marathons. (Round your answer to four decimal places.)

• Part (c)

  Find the 60th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)
  min

• Part (d)

  Find the median of the average running times.
  min

Answer 1