A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to posses a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary-school can run the mile in less than 335 seconds.

Question

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to posses a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary-school can run the mile in less than 335 seconds.

I do not even know what this is asking...can anyone help??

Answer 1

Z = (x - mean)/SD

Solve for Z and look up Z in table in your stats book called something like "areas under the normal distribution" for the smaller portion.

I hope this helps.

Answer 2

To solve this problem, we need to use the properties of a normal distribution. A normal distribution, sometimes referred to as a bell curve, is a continuous probability distribution characterized by its mean and standard deviation.

The problem states that the time for the mile run for boys in secondary school follows a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds.

We want to find the probability that a randomly selected boy can run the mile in less than 335 seconds. In other words, we want to find the probability of a boy's running time being less than 335 seconds.

To find this probability, we can use a Z-score. The Z-score measures the number of standard deviations away from the mean a particular data point is. It is calculated using the formula:

Z = (X - μ) / σ

Where:
- Z is the Z-score
- X is the data point we want to find the probability for (in this case, 335 seconds)
- μ is the mean of the distribution (450 seconds)
- σ is the standard deviation of the distribution (50 seconds)

Let's calculate the Z-score:

Z = (335 - 450) / 50
= -115 / 50
= -2.3

Now, we need to find the probability associated with this Z-score. We can look up this probability in a Z-table or use statistical software.

Using a Z-table, we can find the probability associated with a Z-score of -2.3 (approximately) to be 0.0107.

Therefore, the probability that a randomly selected boy in secondary school can run the mile in less than 335 seconds is approximately 0.0107 or 1.07%.