step 1 Hello, here we have to find the probability that Z is less than 2 .3 or that Z is greater than n

Find P(z<2.3 or z>-1.2)

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Key Concepts

Complement Rule

The complement rule is a foundational concept in probability which states that the probability of an event not occurring is 1 minus the probability of that event occurring. This rule can simplify the calculation of probabilities for unions and intersections by allowing us to consider the complementary event, especially when the direct calculation would be more complex.

Probability of a Union of Events

Calculating the probability of an 'or' event involves determining the union of two events. The probability of the union is typically found using the formula P(A or B) = P(A) + P(B) - P(A and B). This method is important for correctly accounting for any overlap between events, ensuring that shared outcomes are not counted twice.

Standard Normal Distribution

The standard normal distribution is a probability distribution with a mean of 0 and a standard deviation of 1. It is symmetric about the mean and is widely used for creating z-scores, which allow the transformation of any normal distribution to a common scale. This concept underlies methods for calculating probabilities associated with various intervals of z-values.

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