Answer:
A) 0.0107
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 440 seconds and a standard deviation of 40 seconds.
This means that ![\mu = 440, \sigma = 40](https://tex.z-dn.net/?f=%5Cmu%20%3D%20440%2C%20%5Csigma%20%3D%2040)
Find the probability that a randomly selected boy in secondary school can run the mile in less than 348 seconds.
This is the p-value of Z when X = 348. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{348 - 440}{40}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B348%20-%20440%7D%7B40%7D)
![Z = -2.3](https://tex.z-dn.net/?f=Z%20%3D%20-2.3)
has a p-value of 0.0107, and thus, the correct answer is given by option A.