For a standard normal distribution, find:
\[
P(z> 1.77)
\]

Express the probability as a decimal rounded to 4 decimal places.

Question Help:
Video

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 data point is from the mean. Here, we are asked to find the probability that the z-score is greater than 1.77.

Step 2 ：In a standard normal distribution, the total area under the curve is 1, representing the total probability. The area to the left of the z-score represents the cumulative probability up to that z-score. Therefore, to find the probability that z > 1.77, we need to subtract the cumulative probability up to z = 1.77 from 1.

Step 3 ：We can use the cumulative distribution function (cdf) for the standard normal distribution. The cdf gives the probability that a random variable is less than or equal to a certain value. So, we can use it to find the cumulative probability up to z = 1.77, and then subtract that from 1 to get the probability that z > 1.77.

Step 4 ：The cumulative probability up to z = 1.77 is 0.9616364296371288.

Step 5 ：Subtracting this from 1 gives the probability that z > 1.77, which is 0.0384.

Step 6 ：Final Answer: The probability that z > 1.77 in a standard normal distribution is \(\boxed{0.0384}\).