Final answer:
The area in the right tail more extreme is the probability of a value being larger than a specific point, calculated as 1 minus the area to the left of that point. Statistical tools and z-tables can help find this area, crucial for right-tailed hypothesis tests in probability and statistics.
Step-by-step explanation:
To find the area in the right tail that is more extreme, you need to understand the concept of tail areas in probability distributions. The right-tail area of a distribution is the probability of finding a value greater than a certain point (x), denoted as P(X > x). To find this area, first determine P(X < x), which is the area to the left of x under the probability curve. Then, subtract this value from 1 to get the right-tail area: P(X > x) = 1 - P(X < x). For continuous distributions, P(X < x) is equivalent to P(X ≤ x), and similarly, P(X > x) is the same as P(X≥ x).
In a practical context, such as comparing gas trends or testing distributions like American families versus far western U.S. families distributions, these areas help in hypothesis testing, particularly in right-tailed tests. Tools such as z-tables, probability calculators, or normal distribution tables can assist in finding these areas accurately. For example, to find the value z0.01, where the area under the normal density curve to the right is 0.01, you would use a z-table or technology to determine that z0.01 = 2.326, meaning 99% of the area under the curve is to the left of this score.