The University Entrance scores are normally distributed with a mean of 250 and a standard deviation of 30. What is the probability that a randomly selected student scored lower than 250?

To find the probability that a randomly selected student scored lower than 250, we need to calculate the area under the normal distribution curve to the left of this value. This can be done by standardizing the value using the z-score formula and then looking up the corresponding probability in a standard normal distribution table.

First, we need to calculate the z-score:

Z = (X - μ) / σ

where X is the score (250 in this case), μ is the mean (250), and σ is the standard deviation (30).

Z = (250 - 250) / 30 = 0 / 30 = 0

The z-score of 0 means that the value is exactly at the mean.

We know that the area to the left of the mean in a standard normal distribution is 0.5, so the probability of a randomly selected student scoring lower than 250 is also 0.5 or 50%.

Therefore, the probability that a randomly selected student scored lower than 250 is 0.5 or 50%.