I have seen more than 3 different answers for this question on your website. I a

Question

I have seen more than 3 different answers for this question on your website. I am not sure which one, if any, is correct. PLEASE DO NOT COPY YOUR ANSWER FROM ANOTHER. Can you show me every step?

Here is the question:

Over 10,000 runners competed in a large urban marathon. The times of the runners follow a normal distribution. Using the information given below determine the means and the standard deviation for the runners' times. Give your answers in hours,minutes,and seconds.

-Given 16% of the runners were able to finish in less than 3hr 43min 31secs

-Given 97.5% of the runners needed at least 2hr 54min 54sec to complete the marathon

What is the mean? What is the standard deviation?

********Please give your answer in hours AND minutes AND seconds. Not just hours.*************

Explanation / Answer

Lets assume mean = m ; sd= s
half the runners finished in less than some mean time

---- 16% runners finished in fewer than 3.725 hours, i.e.1s below the mean.

So, mean is greater than 3.725 hours.
---- 2.5% runners finished in fewer than 2.915 hours i.e. 1.96s below the mean
Therefore, 0.810 hrs is 0.96s

So, 0.844 hours is the standard deviation which is equal to 50min and 38 sec
So, mean 4.569 hours which is equal to 4 hrs 34 min and 8 seconds.

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