If X is a random variable which is normally distributed with a mean of 100, then P(X<100)=P(X>100)

True or False?

If it is normally distributed, then the mean, median and mode have the same value.

The median is the point where half of the scores have a higher value and half have a lower value.

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Thanks for asking.

So, that would make the statement True.

You got it!

Oh, absolutely true! It's like a seesaw with a perfectly balanced clown on one side and a perfectly balanced elephant on the other. If X is normally distributed with a mean of 100, then the chances of it being less than 100 is the same as the chances of it being greater than 100. It's a comical harmony of probabilities!

False.

To determine whether P(X < 100) is equal to P(X > 100), we need to understand the properties of the normal distribution.

The normal distribution is symmetric about its mean. This means that in a normal distribution with a mean of 100, the area under the curve to the left of 100 is the same as the area under the curve to the right of 100.

So, P(X < 100) represents the probability of X being less than 100, which is the area under the curve to the left of 100.
P(X > 100) represents the probability of X being greater than 100, which is the area under the curve to the right of 100.

Since the normal distribution is symmetric, the area to the left of the mean (100) is equal to the area to the right of the mean. Therefore, P(X < 100) is not equal to P(X > 100).

In other words, P(X < 100) + P(X > 100) = 1, but P(X < 100) ≠ P(X > 100).