_______ per cent of a population will lie between (+ or –) 1.96 standard errors of the population mean. 503595 15

The question seems to be asking about the concept of standard errors in statistics, specifically in relation to the normal distribution.

In a normal distribution, approximately 95% of the population will lie within ±1.96 standard errors of the population mean. This is based on the empirical rule, or 68-95-99.7 rule, which states that in a normal distribution, about 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Here, 1.96 is approximately equal to 2 (standard deviations), hence about 95% of the population will lie within this range.

However, the numbers 503595 and 15 at the end of your question are not clear. If you could provide more context or clarify, I would be able to give a more accurate answer.