Find the indicated $z$ score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. The left shaded area is 0.2033 The indicated $z$ score is $\square$ (Round to two decimal places as needed.)

Step 1 ：The question is asking for the z-score that corresponds to a left-tail probability of 0.2033 in a standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1. The z-score is a measure of how many standard deviations an element is from the mean. In this case, we need to find the z-score such that the area to the left of it under the standard normal curve is 0.2033.

Step 2 ：We can use the inverse of the cumulative distribution function (CDF) of the standard normal distribution to find this z-score. The CDF gives the probability that a random variable is less than or equal to a certain value. The inverse of the CDF, also known as the quantile function, gives the value below which a given percentage of the data falls.

Step 3 ：The z-score that corresponds to a left-tail probability of 0.2033 in a standard normal distribution is approximately -0.83. This means that approximately 20.33% of the data falls below -0.83 standard deviations from the mean in a standard normal distribution.

Step 4 ：Final Answer: The indicated z score is \(\boxed{-0.83}\).