Final answer:
To determine the probability that 'x' will differ from the mean by more than 0.9, further information such as mean, standard deviation, and distribution type is required. In statistical practices, this is usually determined by calculating the area beyond the specified range in the respective distribution, often using technology such as calculators or statistical software.
Step-by-step explanation:
The approximate probability that 'x' will differ from by more than 0.9 can be interpreted in different contexts depending on the given data or distribution. However, based on the samples provided, it's unclear what the exact mean or standard deviation is to use these values directly. To calculate this probability accurately, one would require additional information such as the mean, standard deviation, and the distribution type that 'x' follows, such as a normal distribution.
In general, if 'x' follows a normal distribution, the probability can be obtained by integrating the tails of the distribution, beyond 0.9 units from the mean, using a standard normal distribution table or technology such as a TI-83 or TI-84 calculator. For example, if 'x' has a mean of μ and standard deviation of σ, the z-scores for 'x' ± 0.9 would be calculated as (x ± 0.9 - μ) / σ. These z-scores could then be used to find the corresponding probabilities from the standard normal distribution table.