Step 1 :The standard normal distribution is a special case of the normal distribution. It is the distribution that occurs when a normal random variable has a mean of zero and a standard deviation of one. The z-score is the number of standard deviations a given proportion is away from the mean. To find the area to the left of a certain z-score (which is the same as finding the probability that a value is less than that z-score), we can use the cumulative distribution function (CDF) for a standard normal distribution.
Step 2 :Given that the z-score is \(-0.64\), we can find the area to the left of this z-score under the standard normal curve.
Step 3 :The area to the left of \(z=-0.64\) under the standard normal curve is approximately \(0.26108629969286157\).
Step 4 :Rounding this to four decimal places, we get \(0.2611\).
Step 5 :Final Answer: The area to the left of \(z=-0.64\) under the standard normal curve is \(\boxed{0.2611}\).