The cumulative standardized normal distribution is a function that gives you the probability that a standard normal random variable is less than or equal to a given z-value. In this case, we are looking for the value of z for which the cumulative distribution function (CDF) equals 0.8770.
To find this z-value, you can use a standard normal distribution table, also known as a z-table, or apply statistical software or a calculator that provides the inverse of the CDF for the standard normal distribution.
From the z-table, we can look for the value that is closest to 0.8770. When checking the table, we find that the z-value corresponding to 0.8770 is approximately 1.15. This means that 87.70% of the values under the standard normal curve fall below a z-score of 1.15.
It’s essential to remember that the standard normal distribution is symmetrical around 0, and the values can be negative as well. However, since we are specifically asked for the positive z-value that gives a cumulative probability of 0.8770, our answer is 1.15.
In summary, when the cumulative standardized normal distribution is 0.8770, the value of z is approximately 1.15.