Is it possible to find the exact value for 40th percentile here? If not, why not?

Because we don’t have the mean and the standard deviation . To guess mean and SD, we will need some higher level statistics concept and a table containing z-scores values and even that value will be an estimate .

Yes, you cannot know it. The only thing you know is that it will be more than 400 and less than 500. If it were evenly distributed the value would be 400 (right in the middle between 300 and 400), yet since it is normally distributed the values tend to cluster near the mean, implying that the value we look for will be above 400.

As we see in this picture, we lack the value of \mu (mean) and \sigma (standard\ deviation) . The exact value of 40th percentile thus is unable to be produced.

@sisi I guess we know the mean which is 50 percentile value but I think we don’t know SD hence we can’t calculate.

The mean is at x axis, whereas the value in this question is a value at y axis. They are not the same.

@sisi correct the value for 50th percentile in x axis has a y value of 500 hence it’s same as the mean

@HoldMyBeer @bookworm @sisi OK, so we need the mean and SD… Thank you all!