Question

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours. What is the standard error for the mean finish time of 30 randomly selected participants

Answer 1

Answer:

The standard error is  0.0456 for the mean finish time of 30 randomly selected participants.            

Step-by-step explanation:

We are given the following in the question:

Population mean, $\mu$ = 1.67 hours

Population standard deviation, $\sigma$ = 0.25 hours

Sample mean, $\bar{x}$ = 1.59 hours

Sample standard deviation, s = 0.30 hours

Sample size, n = 30

We have to find the standard error for the mean finish time of 30 randomly selected participants.

Formula:

$\text{Standard error} = \dfrac{\sigma}{\sqrt{n}} = \dfrac{0.25}{\swqrt{30}} = 0.0456$

Thus, the standard error is  0.0456 for the mean finish time of 30 randomly selected participants.