Suppose that we model the distribution of IQ scores in the general population as a normal random variable with mean 100 and standard deviation 15. Find the probability that a randomly selected person's IQ score is between 125 and 130.
I know that an IQ score of 130 is 2 standard deviations away from the mean and 125 is 1.666 standard deviations away. I also know that if X has the standard normal distribution, then σ⋅X+μ has the normal distribution with mean μ and standard deviation σ, for any real μ and any σ>0.
I calculated the z-score for each and they are .9772 and .9515 respectively. However, I am supposed to make sure that at least 6 digits after the decimal point are correct, so my answer of .0257 does not suffice. Is my thinking correct? And if so, how would I get an answer with more decimal places for my answer?