Let X be a random variable with the standard normal distribution. Find: P(- 0.5 < X < 0.5)
To find P(-0.5 < X < 0.5), we first need to find the cumulative distribution function (CDF) of the standard normal distribution at -0.5 and 0.5, and then subtract the two values.
Using a standard normal distribution table or a calculator, we can find that the CDF at -0.5 is approximately 0.3085 and at 0.5 is approximately 0.6915.
Therefore, P(-0.5 < X < 0.5) = P(X < 0.5) - P(X < -0.5)
= 0.6915 - 0.3085
= 0.383
So, P(-0.5 < X < 0.5) ≈ 0.383.