In Problems 5–12, find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found.
Determine the area under the standard normal curve that lies to the right of


a. z = –3.49

Verified step by step guidance

1. Understand that the problem asks for the area under the standard normal curve to the right of z = -3.49. The standard normal curve is symmetric with mean 0 and standard deviation 1.
2. Recall that the total area under the standard normal curve is 1, representing the total probability.
3. Use the standard normal distribution table (Z-table) or a calculator to find the cumulative area to the left of z = -3.49. This value represents \(P(Z \leq -3.49)\).
4. Since the problem asks for the area to the right of z = -3.49, calculate this by subtracting the cumulative area to the left from 1: \(P(Z > -3.49) = 1 - P(Z \leq -3.49)\).
5. Draw a standard normal curve, mark the point z = -3.49 on the horizontal axis, and shade the region to the right of this point to visually represent the area you are calculating.

Key Concepts

Standard Normal Distribution

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is symmetric and bell-shaped, used to find probabilities and areas under the curve corresponding to z-scores.

Z-Score

A z-score represents the number of standard deviations a data point is from the mean. It standardizes values, allowing comparison across different normal distributions and enabling the use of standard normal tables.

Area Under the Curve

The area under the standard normal curve corresponds to probabilities. Finding the area to the right of a given z-score means calculating the probability that a value is greater than that z-score, often using z-tables or technology.