Question

The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. what is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? use the portion of the standard normal table below to help answer the question.

Answer 1

The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes is 0.16 or 16%.

What is normally distributed data?

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data.

The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

The times of the runners in a marathon are normally distributed, with

• Mean of 3 hours and 50 minutes
• Standard deviation of 30 minutes.

Refere the probabiliity table attached below. The probability of Z being inside the 1 Standard daviation of mean is 0.84.

The probability of runner selected with time less than or equal to 3 hours and 20 minutes,

$P=1-0.84\\P=0.16$

Thus, the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes is 0.16 or 16%.

Learn more about the normally distributed data here;

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