Final answer:
The probability corresponding to a z-score can be found by looking at the z-table and subtracting from 1 if necessary. The example gives a z-score area to the left of 0.6554, and after subtraction from 1, we get a decimal probability of 0.3446, which is the fraction sought.
Step-by-step explanation:
Understanding Z-scores and Probabilities
The student's question regards the conversion of a fraction, represented by a z-score, into a decimal. Specifically, the question may relate to finding the probability P(x > 65) where x could represent any measurable attribute, and '65' is a value on the scale of that attribute. The provided z-table value tells us that the area to the left of z is 0.6554. To find the area to the right (which represents the probability of x being greater than 65), we subtract this value from 1, which yields 0.3446. This is the probability, or fraction, we sought to express as a decimal. However, the problem statement seems incomplete as we do not have an option that matches exactly 0.3446, but it’s important to understand the method to arrive at the answer to such questions.
Additionally, the notion of a z-score is essential in statistics as it represents the number of standard deviations an element is from the mean. For example, a z-score of 2.78 signifies that the value is 2.78 standard deviations above the mean. Understanding these concepts is crucial in probability and statistics, and they often come up in various situations, such as constructing confidence intervals, finding percentiles, and calculating probabilities in the context of the normal distribution.