Answer :

To find the probability to the right of a given z-score, we first need to understand what a z-score represents. A z-score measures how many standard deviations an element is from the mean in a standard normal distribution.

In this case, we have a z-score of -1.57, and we need to find the probability to the right of this z-score.

1. Understand the Standard Normal Distribution: The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. The total area under this curve is 1, representing a probability of 100%.

2. Find the Cumulative Probability: For any given z-score, the cumulative probability refers to the area under the curve to the left of that z-score. For a z-score of -1.57, we'll look up this value in a z-table or calculate it using a function that provides cumulative probabilities for standard normal distributions.

- For a z-score of -1.57, the cumulative probability to the left (area under the curve to the left of -1.57) is approximately 0.0582.

3. Calculate the Probability to the Right: Since the total area under the curve is 1, the probability to the right is 1 minus the cumulative probability to the left.

[tex]\[
\text{Probability to the right} = 1 - \text{Cumulative Probability to the left}
\][/tex]

Substituting the values, we get:

[tex]\[
\text{Probability to the right} = 1 - 0.0582 = 0.9418
\][/tex]

Hence, the probability to the right of the z-score -1.57 is approximately 0.9418.

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