An unusual cause of shoulder pain and weakness

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value =...

Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...

Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a...

The muscles surrounding the shoulder girdle, including the clavicle and scapula, primarily stabilize the scapula. This stable base allows other muscles to move the humerus effectively. Scapular movements often mirror those of the humerus and extend its range of motion. For instance, raising the arm above the head would not be feasible without simultaneous upward rotation of the scapula.
Anterior Thoracic Muscles
The anterior thoracic muscles include the serratus anterior, subclavius, and...

The z score is one of the three measures of relative standing. It describes the location of a value in a dataset relative to the mean. z scores are obtained after the standardization of the values in a dataset. The z score for the mean is 0.
 This score indicates how far a value is from the mean in terms of standard deviation. For example, if a data value has a z score of +1, the researcher can infer that the particular data value is one standard deviation above the mean. If another data...

Weak acids and bases do not undergo dissociation completely, and titrations between these two are rarely studied. When such studies are performed, say, for the titration of a weak acid with a weak base, the titration curve plots the change in pH as a function of the volume of base added. Take the titration of acetic acid with ammonia, for instance. During the titration, these two species form ammonium acetate and water, but the pH change is slow and gradual.
As a result, there is no simple...