Question

The times of the finishers in the New York City 10km run are normally distributed with mean of 61 minutes and standard deviation ? minutes. It is known that 70% of finishers have a finish time greater than 60 minutes. Let ?denote the finishing time for finishers in this race.

Note: Show your R codes/output.

Note: You can use the functions pnorm() or qnorm() in R to help you in solving the following parts.

The function pnorm(), compute probabilities from known bounding values. The function qnorm() , aims to do the opposite: given an area, find the boundary value that determines this area.

a) (2 points) Find the standard deviation of the finishing time (?).
Note: Provide the R code and output for the z-value or finding area under the standard normal curve.

b) (2 points) In 2013 approximately 7748 individuals took part in the run. A random sample of 9 individuals is drawn and their finishing times are recorded. Assuming everyone finished the run. What is the probability that among the 9 finishers selected their average finishing time is greater than 59 minutes. Note: Mention the R code and output for the z-value or finding area under the standard normal curve. Do the calculations for 3 decimal points.

c) (2 points) A second, independent sample of individuals is drawn from this population. How large of a sample must be drawn if the probability that the average finishing time is less than 62 must be 80%? Note: Show the R code and output for the z-value or for finding area under the standard normal curve.

Answer 1

the times of the finishers in the new york city 10km run are normally distributed with mean of 61 minutes and standard devition mintes.